Question

Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable. (If an answer does not exist, enter DNE.) g(x) = x3 − 15x

Answer 1

We have the function g(x) = x^3 -15*x

First, to find extrema, we can find the zeros of the first derivative.

g'(x) = 3*x^2 -15

g'(x) = 0 = 3*x^2 - 15

x^2 = 15/3 = 5

x = √5

x = -√5

Now, watching at the second derivative we have:

g''(x) = 6*x

so when we have

g''(√5) = 6*√5 > 0 then x = √5 is a local minimum

g''(-√5) = -6*√5 < 0, then x = -√5 is a local maximum.