Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

Key Questions

• How do you know a function is increasing?

  Answer:

  It will be increasing when the first derivative is positive.

  Explanation:

  Take the example of the function `f(x) = e^(x^2 - 1)`.

  The first derivative is given by `f'(x) = 2xe^(x^2 - 1)` (chain rule). We see that the derivative will go from increasing to decreasing or vice versa when `f'(x) = 0`, or when `x= 0`.

  Whenever you have a positive value of `x`, the derivative will be positive, therefore the function will be increasing on `{x|x> 0, x in RR}`.

  The graph confirms

  Hopefully this helps!

  Noah G · 1 · Mar 9 2018
• What is the meaning of monotonically increasing function?

  Answer:

  If `x_0 < x_1` then `f(x_0) < f(x_1)`

  Explanation:

  The meaning is that you have a function with positive slope in every point of Dom.

  Starting from a `x_0` and move to right, the graph of function is moving up at the same time

  F. Javier B. · 1 · May 24 2018

• How do you know a function is increasing?
• What is the meaning of monotonically increasing function?
• How do you find all intervals where the function `f(x)=1/3x^3+3/2x^2+2` is increasing?
• How do you find all intervals where the function `f(x)=e^(x^2)` is increasing?
• What is the derivative graph of a parabola?
• If `f(x) = 2x^3 + 3x^2 - 180x`, how do I find the intervals on which f is increasing and decreasing?
• Suppose that I don't have a formula for `g(x)` but I know that `g(1) = 3` and `g'(x) = sqrt(x^2+15)` for all x. How do I use a linear approximation to estimate `g(0.9)` and `g(1.1)`?
• What information does the first derivative tell you?
• How do you find the interval in which the function `f(x)=2x^3 + 3x^2+180x` is increasing or decreasing?
• How do you find values of t in which the speed of the particle is increasing if he position of a particle moving along a line is given by `s(t)=2t^3-24t^2+90t+7` for `t≥0`?
• How do you know a function is decreasing or increasing at `x=1` given the function `4x^2-9x`?
• Is `f(x)=x^2-x` increasing or decreasing at `x=1`?
• Is `f(x)=x^2(x-2)-3x` increasing or decreasing at `x=1`?
• Is `f(x)=1/(x-1)-1/(x+1)^2` increasing or decreasing at `x=0`?
• Is `f(x)=x-sqrt(x^3-3x)` increasing or decreasing at `x=2`?
• Is `f(x)=x-1/sqrt(x^3-3x)` increasing or decreasing at `x=2`?
• Is `f(x)=3x^2-x+4` increasing or decreasing at `x=2`?
• Is `f(x)=-4x^2+x-1` increasing or decreasing at `x=1`?
• Is `f(x)=-x^2+3x-1` increasing or decreasing at `x=1`?
• Is `f(x)=-2x^2-2x-1` increasing or decreasing at `x=-1`?
• Is `f(x)=-x^3+3x^2-x+2` increasing or decreasing at `x=-1`?
• Is `f(x)=-2x^3+2x^2-x+2` increasing or decreasing at `x=0`?
• Is `f(x)=-2x^3+4x^2-3x-1` increasing or decreasing at `x=0`?
• Is `f(x)=-7x^3+x^2-2x-1` increasing or decreasing at `x=-2`?
• Is `f(x)=-3x^3-5x^2-x-1` increasing or decreasing at `x=-2`?
• Is `f(x)=-x^3-2x^2-3x-1` increasing or decreasing at `x=2`?
• Is `f(x)=-4x^3+4x^2+2x-1` increasing or decreasing at `x=2`?
• Is `f(x)=-4x^3+x^2+2x+2` increasing or decreasing at `x=2`?
• Is `f(x)=-12x^3+17x^2+2x+2` increasing or decreasing at `x=2`?
• Is `f(x)=-2x^3-5x^2-6x-1` increasing or decreasing at `x=1`?
• Is `f(x)=(x-3)(x+3)(x-2)` increasing or decreasing at `x=1`?
• Is `f(x)=(x-3)(x+3)(x-2)` increasing or decreasing at `x=3`?
• Is `f(x)=(x+2)(2x-3)(x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(x+1)(2x-3)(3x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(x+1)(x+2)(x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(x+3)(x-2)(x+4)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x+3)(x-2)(x-2)` increasing or decreasing at `x=-2`?
• Is `f(x)=(2x+3)(x-6)(x-2)` increasing or decreasing at `x=-2`?
• Is `f(x)=(x+3)(x-6)(x/3-1)` increasing or decreasing at `x=-2`?
• Is `f(x)=(x+7)(x-2)(x-1)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x-4)(x-12)(x/4-1)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x-16)(x-12)(x/4+3)` increasing or decreasing at `x=1`?
• Is `f(x)=(x-1)(x-1)(x-3)` increasing or decreasing at `x=1`?
• Is `f(x)=(x+3)(x-8)(x-3)` increasing or decreasing at `x=1`?
• Is `f(x)=(x+1)(x-4)(x-2)` increasing or decreasing at `x=1`?
• Is `f(x)=(x+1)(x+5)(x-7)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x-3)(x+11)(x-7)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x-3)(x+15)(x+2)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x-3)(x+5)(x+2)` increasing or decreasing at `x=-3`?
• Is `f(x)=(x-2)(x+5)(x+2)` increasing or decreasing at `x=-3`?
• Is `f(x)=(x-2)(x+5)(x-1)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x-2)(2x-3)(2x-1)` increasing or decreasing at `x=-2`?
• Is `f(x)=(x-1)(x-3)(2x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(x+3)(x-3)(3x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(x-2)(x+1)(x+4)` increasing or decreasing at `x=1`?
• Is `f(x)=(2x-2)(x+1)(x+4)` increasing or decreasing at `x=-1`?
• Is `f(x)=(2x-2)(x+1)(x+4)` increasing or decreasing at `x=1`?
• Is `f(x)=(x-2)^2(x+1)(x+4)` increasing or decreasing at `x=1`?
• Is `f(x)=(x-2)^2(x+1)` increasing or decreasing at `x=1`?
• Is `f(x)=(x-2)^2(x-1)` increasing or decreasing at `x=1`?
• Is `f(x)=(x-2)^2/(x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(x-2)^2/(x+1)` increasing or decreasing at `x=2`?
• Is `f(x)=(x^2-2)/(x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(x^2-2)/(x+1)` increasing or decreasing at `x=1`?
• Is `f(x)=(x^2-3x-2)/(x+1)` increasing or decreasing at `x=1`?
• Is `f(x)=(x^2-3x-2)/(x^2+1)` increasing or decreasing at `x=1`?
• Is `f(x)=(x^2-4x-2)/(x^2+1)` increasing or decreasing at `x=-3`?
• Is `f(x)=(-2x^2-4x-2)/(2x^2+1)` increasing or decreasing at `x=-3`?
• Is `f(x)=(-x^2-5x-2)/(x^2+1)` increasing or decreasing at `x=-3`?
• Is `f(x)=(-x^2+5x-2)/(x^2-1)` increasing or decreasing at `x=-3`?
• Is `f(x)=(-x^2+3x+2)/(x^2-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(-3x^2-3x+2)/(x^2+3)` increasing or decreasing at `x=1`?
• Is `f(x)=(-3x^2-3x-2)/(x^2+x)` increasing or decreasing at `x=1`?
• Is `f(x)=(-3x^2-x+2)/(x^2+x)` increasing or decreasing at `x=1`?
• Is `f(x)=(-x^3-2x^2-x+2)/(x^2+x)` increasing or decreasing at `x=1`?
• Is `f(x)=(-x^3-x^2-x+2)/(x^2+3x)` increasing or decreasing at `x=1`?
• Is `f(x)=(-7x^3-x^2-2x+2)/(x^2+3x)` increasing or decreasing at `x=1`?
• Is `f(x)=(-5x^3-x^2+2x-2)/(-x+3)` increasing or decreasing at `x=1`?
• Is `f(x)=(-2x^3+4x^2-x-2)/(x+3)` increasing or decreasing at `x=-2`?
• Is `f(x)=(x^3+2x^2-x-2)/(x+3)` increasing or decreasing at `x=-2`?
• Is `f(x)=(x^3+3x^2-x-9)/(x+1)` increasing or decreasing at `x=-2`?
• Is `f(x)=(x^3+3x^2-4x-9)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3-6x^2-4x-9)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^2-4x-9)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^2-5x-9)/(2x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^2+2x-6)/(2x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^2+2x-2)/(2x-4)` increasing or decreasing at `x=0`?
• Is `f(x)=(-2x^2-5x-2)/(2x-4)` increasing or decreasing at `x=0`?
• Is `f(x)=(-2x^2-15x-12)/(2x-4)` increasing or decreasing at `x=0`?
• Is `f(x)=(-12x^2-22x-2)/(x-4)` increasing or decreasing at `x=1`?
• Is `f(x)=(-x^2-2x-2)/(x-3)` increasing or decreasing at `x=1`?
• Is `f(x)=(x^2-6x-12)/(x+2)` increasing or decreasing at `x=1`?
• Is `f(x)=(12x^2-16x-12)/(x+2)` increasing or decreasing at `x=5`?
• Is `f(x)=(6x^2-x-12)/(x+3)` increasing or decreasing at `x=3`?
• Is `f(x)=(x^3-4x^2-4x+5)/(x+2)` increasing or decreasing at `x=3`?
• Is `f(x)=(3x^3-2x^2-2x+5)/(x+2)` increasing or decreasing at `x=3`?
• Is `f(x)=(-x^3-2x^2-12x+2)/(x-4)` increasing or decreasing at `x=3`?
• Is `f(x)=(-x^3-7x^2-x+2)/(x-2)` increasing or decreasing at `x=3`?
• Is `f(x)=(3x^3+3x^2+5x+2)/(x-2)` increasing or decreasing at `x=3`?
• Is `f(x)=(3x^3+x^2-2x+7)/(2x-2)` increasing or decreasing at `x=3`?
• Is `f(x)=(-x^3+x^2-x+7)/(x-2)` increasing or decreasing at `x=-1`?
• Is `f(x)=(-x^3+2x^2-3x+7)/(x-2)` increasing or decreasing at `x=-1`?
• Is `f(x)=(4x^3+2x^2-2x-3)/(x-2)` increasing or decreasing at `x=-1`?
• Is `f(x)=(4x^3-2x^2-x-3)/(x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3-2x^2+5x-4)/(x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3+7x^2-5x-4)/(x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3-4x^2+3x-4)/(4x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(-2x^3+3x^2+3x-4)/(4x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(-2x^3+x^2-2x-4)/(4x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3+x^2+2x-4)/(4x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(-x^3+x^2-3x-4)/(4x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(-x^3+x^2-5x+6)/(x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(-2x^3+9x^2-5x+6)/(x-2)` increasing or decreasing at `x=0`?
• Is `f(x)=(-2x^3-6x^2-3x+2)/(2x-1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3-5x^2-x+2)/(2x-1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3-3x^2-5x+2)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(-2x^3-x^2-5x+2)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(-x^3-x^2+2x+2)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3-9x^2+12x+2)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(x^3+5x^2-7x+2)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(4x^3+5x^2-2x+7)/(x+1)` increasing or decreasing at `x=0`?
• Is `f(x)=(2x^3+5x^2-9x+1)/(x-4)` increasing or decreasing at `x=0`?
• Is `f(x)=(-3x^3+15x^2-2x+1)/(x-4)` increasing or decreasing at `x=2`?
• Is `f(x)=(2x^3+2x^2+2x+1)/(x-3)` increasing or decreasing at `x=2`?
• Is `f(x)=(2x^3-7x^2+3x+1)/(x-3)` increasing or decreasing at `x=2`?
• Is `f(x)=(2x^3-7x^2+13x-11)/(x-3)` increasing or decreasing at `x=2`?
• Is `f(x)=(3x^3-5x^2+13x-11)/(x-3)` increasing or decreasing at `x=2`?
• Is `f(x)=(-5x^3-x^2-3x-11)/(x-3)` increasing or decreasing at `x=2`?
• Is `f(x)=(-5x^3+x^2-3x-11)/(x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(-x^3+x^2+2x-11)/(x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(3x^3+x^2-2x-14)/(x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(x^3-4x^2-2x-4)/(x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=1/e^x` increasing or decreasing at `x=0`?
• Is `f(x)=xe^x` increasing or decreasing at `x=0`?
• Is `f(x)=x/(2-e^x)` increasing or decreasing at `x=0`?
• Is `f(x)=x^2lnx` increasing or decreasing at `x=1`?
• Is `f(x)=x^2-3lnx` increasing or decreasing at `x=1`?
• Is `f(x)=x/(x+x^2)-lnx` increasing or decreasing at `x=1`?
• Is `f(x)=x(lnx)^2` increasing or decreasing at `x=1`?
• Is `f(x)=xln(x)^2` increasing or decreasing at `x=1`?
• Is `f(x)=sqrt(ln(x)^2)` increasing or decreasing at `x=1`?
• Is `f(x)=e^x(x^2-x)` increasing or decreasing at `x=3`?
• Is `f(x)=e^xsqrt(x^2-x)` increasing or decreasing at `x=3`?
• Is `f(x)=e^x/sqrt(x^2-x)` increasing or decreasing at `x=3`?
• Is `f(x)=e^(x^2-x)-x^2` increasing or decreasing at `x=3`?
• Is `f(x)=e^(x^2-x)(x^2-x)` increasing or decreasing at `x=2`?
• Is `f(x)=e^(x^2-x)/(x^2-x)` increasing or decreasing at `x=2`?
• Is `f(x)=(1-e^x)/x^2` increasing or decreasing at `x=2`?
• Is `f(x)=(1-e^x)/(1-x^2)` increasing or decreasing at `x=2`?
• Is `f(x)=(1-xe^x)/(1-x^2)` increasing or decreasing at `x=2`?
• Is `f(x)=(x-e^x)/(x-x^2)` increasing or decreasing at `x=2`?
• Is `f(x)=(x-xe^x)/(x-1)` increasing or decreasing at `x=2`?
• Is `f(x)=(x-e^x)/(x-1)^3` increasing or decreasing at `x=2`?
• Is `f(x)=e^x/(x-2)` increasing or decreasing at `x=3`?
• Is `f(x)=(x^2e^x)/(x+2)` increasing or decreasing at `x=-1`?
• Is `f(x)=(x^2-e^x)/(x-2)` increasing or decreasing at `x=-1`?
• Is `f(x)=sinx-cosx` increasing or decreasing at `x=0`?
• Is `f(x)=cos(-x)` increasing or decreasing at `x=0`?
• Is `f(x)=tanx` increasing or decreasing at `x=0`?
• Is `f(x)=tanx-sinx` increasing or decreasing at `x=pi/3`?
• Is `f(x)=cosx*sinx` increasing or decreasing at `x=pi/3`?
• Is `f(x)=cscx-sinx` increasing or decreasing at `x=pi/3`?
• Is `f(x)=x-e^xsinx` increasing or decreasing at `x=pi/3`?
• Is `f(x)=x-e^x/sinx` increasing or decreasing at `x=pi/3`?
• Is `f(x)=sinx/x` increasing or decreasing at `x=pi/3`?
• Is `f(x)=sinx/e^x` increasing or decreasing at `x=pi/3`?
• Is `f(x)=cosx/e^x` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cosx/(pi-e^x)` increasing or decreasing at `x=pi/6`?
• Is `f(x)=e^-xcos(-x)-sinx/(pi-e^x)` increasing or decreasing at `x=pi/6`?
• Is `f(x)=e^-xcos(-x)` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cosx+sinx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cos^2x+sin2x` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cos2x-sin^2x` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cotx-e^xtanx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=e^x+cosx^2` increasing or decreasing at `x=pi/6`?
• Is `f(x)=e^x+cosx-e^xsinx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=e^x/cosx-e^x/sinx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cosx*tanx-sinx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cosx+tanx-sinx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cosx+cotx*sinx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cot(2x)*tanx` increasing or decreasing at `x=pi/6`?
• Is `f(x)=cot(2x)*tanx^2` increasing or decreasing at `x=pi/3`?
• Is `f(x)=cotx*tanx` increasing or decreasing at `x=pi/3`?
• Is `f(x)=sinx-cos(pi-x)` increasing or decreasing at `x=pi/3`?
• Is `f(x)=sin(pi/2-x)-cos(pi-x)` increasing or decreasing at `x=pi/3`?
• Is `f(x)=sin(3x)-cos(2x-pi)` increasing or decreasing at `x=pi/3`?
• Is `f(x)=xe^(x^3-x)-x^3` increasing or decreasing at `x=4`?
• Is `f(x)=xe^(x^3-x)-1/x^3` increasing or decreasing at `x=4`?
• Is `f(x)=x-e^(2x)-1/x^2` increasing or decreasing at `x=2`?
• Is `f(x)=1/x-1/x^3+1/x^5` increasing or decreasing at `x=2`?
• Is `f(x)=1/x-1/x^3+1/x^5` increasing or decreasing at `x=1`?
• Is `f(x)=1/x-1/x^3+1/x^5` increasing or decreasing at `x=-1`?
• Is `f(x)=(1-x)/(x+2)^3` increasing or decreasing at `x=-1`?
• Is `f(x)=(3-e^(2x))/x` increasing or decreasing at `x=-1`?
• Is `f(x)=(1-e^(2x))/(2x-4)` increasing or decreasing at `x=-1`?
• Is `f(x)=(1-e^(2/x))/(2x-4)` increasing or decreasing at `x=-1`?
• Is `f(x)=ln(2x^2-1)` increasing or decreasing at `x=-1`?
• Is `f(x)=-xln(2x^2)` increasing or decreasing at `x=-1`?
• Is `f(x)=-x/(x-5)` increasing or decreasing at `x=-1`?
• Is `f(x)=x^3-2x+4` increasing or decreasing at `x=0`?
• Is `f(x)=x^3+2x-4` increasing or decreasing at `x=0`?
• Is `f(x)=-2x^2-3x+4` increasing or decreasing at `x=-2`?
• Is `f(x)=x^2-3x` increasing or decreasing at `x=-2`?
• Is `f(x)=e^x-3x` increasing or decreasing at `x=-1`?
• Is `f(x)=xe^x-3x` increasing or decreasing at `x=-3`?
• Is `f(x)=xe^x-x^2e^x` increasing or decreasing at `x=0`?
• Is `f(x)=x^2e^x` increasing or decreasing at `x=1`?
• Is `f(x)=e^x` increasing or decreasing at `x=1`?
• Is `f(x)=x/e^x` increasing or decreasing at `x=1`?
• Is `f(x)=(x-2)/e^x` increasing or decreasing at `x=-2`?
• Is `f(x)=(x-2)e^x` increasing or decreasing at `x=-2`?
• Is `f(x)=4xe^x` increasing or decreasing at `x=-2`?
• Is `f(x)=4x-e^(3x-2)` increasing or decreasing at `x=-2`?
• Is `f(x)=4x-e^(x+2)` increasing or decreasing at `x=-1`?
• Is `f(x)=-e^(x^2+2)` increasing or decreasing at `x=0`?
• Is `f(x)=-e^(x^2-3x+2)` increasing or decreasing at `x=0`?
• Is `f(x)=-x/e^(x^2-3x+2)` increasing or decreasing at `x=4`?
• Is `f(x)=sqrt(x+2)` increasing or decreasing at `x=2`?
• Is `f(x)=sqrt(1/x-2)` increasing or decreasing at `x=2 /9`?
• Is `f(x)=1/sqrt(x+3)` increasing or decreasing at `x=3`?
• Is `f(x)=x/sqrt(x+3)` increasing or decreasing at `x=5`?
• Is `f(x)=(x-3)/sqrt(x+3)` increasing or decreasing at `x=5`?
• Is `f(x)=(x-3)/sqrt(x+3)` increasing or decreasing at `x=3`?
• Is `f(x)=sqrt(xe^x+3x)` increasing or decreasing at `x=0`?
• Is `f(x)=3x^3-2x^2` increasing or decreasing at `x=0`?
• Is `f(x)=3x^3-6x-7` increasing or decreasing at `x=0`?
• Is `f(x)=(x-2)^2-6x-7` increasing or decreasing at `x=-2`?
• Is `f(x)=(2x+4)^2-6x-7` increasing or decreasing at `x=-2`?
• Is `f(x)=(x+4)^2+x^2-3x` increasing or decreasing at `x=-2`?
• Is `f(x)=(-x-4)^2+3x^2-3x` increasing or decreasing at `x=-1`?
• Is `f(x)=(x-1)^2+2x^2-3x` increasing or decreasing at `x=-1`?
• Is `f(x)=(x+2)^2-4x^2-3x` increasing or decreasing at `x=-1`?
• Is `f(x)=(x+3)^3-4x^2-2x` increasing or decreasing at `x=0`?
• Is `f(x)=(x-3)^3+3x^2-2x` increasing or decreasing at `x=0`?
• Is `f(x)= 2xsinx` increasing or decreasing at `x=pi/3`?
• Is `f(x)= x/sinx` increasing or decreasing at `x=-pi/6`?
• Is `f(x)= x-12sinx` increasing or decreasing at `x=-pi/6`?
• Is `f(x)= x-12sin(3x-pi/4)` increasing or decreasing at `x=-pi/6`?
• Is `f(x)= x/pi-2sin(3x-pi/4)` increasing or decreasing at `x=-pi/6`?
• Is `f(x)= cos(3x-pi/6)+2sin(4x-(3pi)/4)` increasing or decreasing at `x=pi/12`?
• Is `f(x)=5 cos(3x+(5pi)/6)+ 2sin(4x-(3pi)/4)` increasing or decreasing at `x=pi/12`?
• Is `f(x)= 4sin(4x-(3pi)/4)` increasing or decreasing at `x=pi/12`?
• Is `f(x)= 4sin(4x-(3pi)/8)` increasing or decreasing at `x=pi/12`?
• Is `f(x)= sin(x+(3pi)/8)` increasing or decreasing at `x=pi/12`?
• Is `f(x)= cot(3x+(3pi)/8)` increasing or decreasing at `x=pi/12`?
• Is `f(x)= cot(3x+(5pi)/8)` increasing or decreasing at `x=pi/4`?
• Is `f(x)= cot(-x+(5pi)/6)` increasing or decreasing at `x=pi/4`?
• Is `f(x)= cos(x+(5pi)/6)` increasing or decreasing at `x=pi/4`?
• Is `f(x)= cos(x+(5pi)/4)` increasing or decreasing at `x=-pi/4`?
• Is `f(x)= cos(3x+(5pi)/4)` increasing or decreasing at `x=-pi/4`?
• Is `f(x)= 4xcos(3x-(5pi)/4)` increasing or decreasing at `x=-pi/4`?
• Is `f(x)= cos(2x+(3pi)/4)` increasing or decreasing at `x=-pi/4`?
• Is `f(x)= cos(x+(pi)/4)` increasing or decreasing at `x=pi/3`?
• If `f(x)=sinx-xcosx`, how the function behaves in the intervals `(0,pi)` and `(pi,2pi)` i.e. whether it is increasing or decreasing?
• What interval(s) is `x / (1+x)^2` increasing and decreasing?
• How do you find the absolute maximum and absolute minimum values of f on the given interval: `f(t) =t sqrt(25-t^2)` on [-1, 5]?
• How do you find the absolute maximum and absolute minimum values of f on the given interval: `f(x) = x-ln(3x)` on [0.5, 2]?
• How do you find the intervals of increasing and decreasing given `y=-x^3+2x^2+2`?
• How do you find the intervals of increasing and decreasing given `y=x^3-11x^2+39x-47`?
• How do you find the intervals of increasing and decreasing given `y=-x^4+3x^2-3`?
• How do you find the intervals of increasing and decreasing given `y=x^2/(4x+4)`?
• How do you find the intervals of increasing and decreasing given `y=(3x^2-3)/x^3`?
• How do you find the intervals of increasing and decreasing given `y=(2x-8)^(2/3)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^2-6x+8`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^4-2x^2`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=1/(x+1)^2`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^2-2x-8`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=xsqrt(16-x^2)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x+4/x`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x-2cosx`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^2-4x`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^2+6x+10`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=-2x^2+4x+3`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=-(x^2+8x+12)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=2x^3+3x^2-12x`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=(x-1)^2(x+3)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=(x+2)^2(x-1)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=(x^5-5x)/5`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^4-32x+4`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^(2/3)-4`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=(x+2)^(2/3)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=(x-1)^(1/3)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=5-abs(x-5)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=abs(x+4)-1`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=2x+1/x`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=(x+4)/x^2`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x/2+cosx`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=sinx+cosx`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=cos^2(2x)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=sin^2x+sinx` in `0 ≤ x ≤ (5pi)/2`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=2xsqrt(9-x^2)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=10(5-sqrt(x^2-3x+16))`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=(x^5-4x^3+3x)/(x^2-1)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x(x^2-3)`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=cos^2x-sin^2x`?
• How do you find the intervals of increasing and decreasing using the first derivative given `y=x^3-4x`?
• Question #c66f7
• How do you find the largest open interval where the function is decreasing `f(x)=sqrt(4-x)`?
• Question #932f1
• Question #f729c
• How to prove that (tan b / tab a) > (b/a) whenever 0 < a < b < π/2?
• Question #0f52d
• Question #ed9fd
• (a) Find the interval on which f is increasing and decreasing? (b) Find the local maximum value of f? (c) Find the inflection point? (d) Find the interval on which f is concave up and concave down?
• How to demonstrate that `sqrt(2)^(sqrt(3)-1)>sqrt(3)^(sqrt(2)-1)`?We know that `g:(1,+oo)->RR,g(x)=``(lnx)/(x-1)`,and `g` is decreasing.
• In which interval the function `f(x)=sqrt(x^2+8)-x` is a decreasing function?
• What is the end behaviour of `y = -x^4`?
• Only one option is correct ,Please help ; How to solve this question?
• Another question involving functions and derivates. I solved a third of it but the other two parts are confusing. Can someone help me solve it?