Question

Can someone explain why to use the second derivative in this question.

The question asks for the dimensions of the box with the max value. I found the equation, then the first derivative then its critical points. I was told to sub the critical points of the first derivative into the second derivative to find the max value. Why the second derivative thought? I don't get why I have to use that to find the max value.

Answer 1

in the first derivative we use it to find the points where the function's slope is zero.

In the second derivative we use it to find whether these critical points are min or a max