Differentiable vs. Non-differentiable Functions

Key Questions

• What does differentiable mean for a function?

  geometrically, the function `f` is differentiable at `a` if it has a non-vertical tangent at the corresponding point on the graph, that is, at `(a,f(a))`. That means that the limit
  `lim_{x\to a} (f(x)-f(a))/(x-a)` exists (i.e, is a finite number, which is the slope of this tangent line). When this limit exist, it is called derivative of `f` at `a` and denoted `f'(a)` or `(df)/dx (a)`. So a point where the function is not differentiable is a point where this limit does not exist, that is, is either infinite (case of a vertical tangent), where the function is discontinuous, or where there are two different one-sided limits (a cusp, like for `f(x)=|x|` at 0). See definition of the derivative and derivative as a function.

  Calculus V. · · Jul 25 2014

• What are non differentiable points for a function?
• What does differentiable mean for a function?
• What are non differentiable points for a graph?
• How do you find the non differentiable points for a function?
• How do you find the non differentiable points for a graph?
• What are differentiable points for a function?
• How do you find the differentiable points for a graph?
• What is the derivative of a unit vector?
• On what interval is the function `ln((4x^2)+9)` differentiable?
• How do you find the partial derivative of the function `f(x,y)=intcos(-7t^2-6t-1)dt`?
• How do you solve the differential equation `dy/dt = 2y - 10`?
• What are some examples of non differentiable functions?
• What is the total differential of `z=x^2+2y^2-2xy+2x-4y-8`?
• At where f(x)=|(x^2)-9| is differentiable?
• Can a function be continuous and non-differentiable on a given domain??
• Can a function be continuous and non-differentiable on a given domain?
• How to determine which of the following functions are one-to-one ?
• Question #491a2
• How do you determine the values of x at which `sqrt(x^2 + 9)` is differentiable?
• `inte^x[((sin^-1x)sqrt(1-x^2)+1)/sqrt(1-x^2)]dx` ?
• What is the difference between differentiability and continuity of a function?
• If a function is continuous along the interval [1,3], would it be differentiable at x=1 and x=3?
• If f(x) is continuous and differentiable and `f(x) = ax^4 + 5x`; `x<=2` and `bx^2 - 3x`; x> 2, then how do you find b?
• How do you determine the differentiability of f(x), where `f(x)=|x-1|+|x-2|+|x-3|`?
• Let f(x) be a function satisfying |f(x)| ≤ x^2 for -1 ≤ x ≤ 1, how do you show that f is differentiable at x = 0 and find f’(0)?
• How do you verify whether rolle's theorem can be applied to the function `f(x)=tanx` in [0,pi]?
• How do you verify whether rolle's theorem can be applied to the function `f(x)=absx` in [-1,1]?
• How do you verify whether rolle's theorem can be applied to the function `f(x)=1/x^2` in [-1,1]?
• How do you verify whether rolle's theorem can be applied to the function `f(x)=x^3` in [1,3]?
• How do you prove from the definition of differentiability that the function `f(x)=(2x+1)/(x-2)` is differentiable?
• If there was a hole in the line at (2,3) and there is another point at (2,1), then would the graph be differentiable at that point and why?
• Question #39963
• Given `(dr)/(dt)=(sect,tant,t^2)` calculate `r(t)` such that `r(0) = (0,0,3)` ?
• For what values of x is the function `f(x)=abs(x^2-9)` differentiable?
• Where is the function `h(x)=abs(x-1)+abs(x+2)` differentiable?
• Question #04706
• Given `f(x) = x^3-3x`, how can you construct an infinitely differentiable one-one function `g(x):RR->RR` with `g(x) = f(x)` in `(-oo, -2] uu [2, oo)`?
• Question #602c5
• Question #0b8db
• Question #831b1
• Question #400e8
• Differentiate `sinx` `/` `5x` + `sec^2 x"` ?
• Verify that `f(x)` is differentiable at `x = 0`? `f(x) = x((e^(1//x) - 1)/(e^(1//x) + 1))`
• Integrating factor question?