First Derivative Test vs Second Derivative Test for Local Extrema

Key Questions

• How does the first derivative test differ from the second derivative test?

  Since you are asking for the difference, I assume that you are familiar with how each test works. The biggest difference is that the first derivative test always determines whether a function has a local maximum, a local minimum, or neither; however, the second derivative test fails to yield a conclusion when #y''# is zero at a critical value. If that is the case, you will have to apply the first derivative test to draw a conclusion.

  Wataru · 1 · Sep 24 2014

• What is the first derivative test to determine local extrema?
• How does the first derivative test differ from the second derivative test?
• How does the first derivative test work?
• What is the first derivative test for critical points?
• What is the first derivative test for local extreme values?
• What does the first derivative test tell you?
• How do you know when to use the first derivative test and the second derivative test?
• How do you use the second derivative test to find the local extrema for #f(x)=sin(x)#?
• How do you use the second derivative test to find the local extrema for #f(x)=e^(x^2)#?
• How do you use the second derivative test how do you find the local maxima and minima of #f(x) = 12 + 2x^2 - 4x^4#?
• How do you find the second derivative test to find extrema for #f(x) = 2x^2lnx-5x^2#?
• How do you find the extremas for #f(x)=x^3 - 9x^2 + 27x#?
• How do you use the second derivative test to find the relative maxima and minima of the given #f(x)= x^4 - (2x^2) + 3#?
• Let f'' (x)= 4x^3 - 2x and let f(x) has critical numbers -1, 0, and 1, how do you use the second derivative test to determine which critical numbers, if any give a relative maximum?
• How do you use the second derivative test to find the relative extrema for #h(t) = t-4sqrt(t+1)#?
• If #f '(x) = 8x^3 - 16x#, how do you use the second derivative test to find maximum and minimum?
• Using the second derivative test, how do you find the local maximum and local minimum for #f(x) = x^(3) - 6x^(2) + 5#?
• How do you use the 2nd derivative test to find all relative extrema of #f(x)=(9x^(2)+1)/x#?
• How do you use the Second Derivative Test where applicable to find the extrema for #f(x) = x^2(6-x)^3#?
• How do you find the exact relative maximum and minimum of the polynomial function of #g(x) =x^3 + 6x^2 – 36#?
• How do you find the exact relative maximum and minimum of the polynomial function of #4x^8 - 8x^3+18#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3-6x^2+15#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = 2 csc x#?
• How do you find the value of k for which #f(x)=x^3-5x^2+3x+k# has 11 as its relative minimum?
• How do you find the exact relative maximum and minimum of the polynomial function of #2x^3 -23x^2+78x-72#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=x^3-3x+6#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3 - 6x^2 + 9x +1#?
• How do you find the exact relative maximum and minimum of the polynomial function of #x^4+x^3-6x^2-4x+8#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=(x^3)-12x+2#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3 - 2x^2 - x +1#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=4x-x^2#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3 - 3x^2 - x + 1#?
• How do you find the exact relative maximum and minimum of the polynomial function of #y=x^2 +x -1#?
• How do you find the exact relative maximum and minimum of the polynomial function of #y=x^2+1#?
• How do you find the exact relative maximum and minimum of the polynomial function of #y=2-x^2#?
• How do you find the exact relative maximum and minimum of the polynomial function of #y=x^3#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)= 2x^3-3x^2-12x-1#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3 + 4x^2 - 5x#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) =2x^3-3x^2-12x#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)= x^2-4x-5#?
• How do you find the exact relative maximum and minimum of the polynomial function of #x^3+3x^2-5x=f(x)#?
• How do you find the exact relative maximum and minimum of the function of #f(x) = 4x+6x^-1#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3 + x + 4/x#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f (x) = x^3 - 6x^2 - 15x + 11#?
• How do you find the absolute maximum and minimum of the polynomial function of #f(x) = 2x^3 – 6x^2 – 48x + 24#?
• How do you find the exact relative maximum and minimum of the polynomial function of # f(x) = –2x^3 + 6x^2 + 18x –18 #?
• How do you find the exact relative maximum and minimum of the polynomial function of #p(x) =80+108x-x^3 #?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=2x^3+3x^2-12x #?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=2x^3+x^2-11x#?
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=x^3+6x^2-36x#?
• How do you find the inflection point and concavity of #f(x)=x^(4)*ln (x)#?
• Question #fcd99
• How do you find the maximum or minimum of #f(x)=x^2+6x-2#?
• For what value of #k# will #x+k/x# have a relative maximum at #x=2#?
• Find the maximum and minimum values for the function #f# defined by #f(x) = 2sinx + cos2x# in the interval #[0, pi/2]#?