Please show step-by-step solutions for me to understand. I need to be able to understand how to solve this problem so please make it step-by-step. I will appreciate it. Thank you so much! Have a great day ahead!

Suppose that f is a function such that f' (c) = 1 for some number c in the interval [(1, b]. Is it possible for f (c) to be an absolute extremum on [(1, b]? Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and four sides cost Php 10/112, and the material for the bottom cost Php 20/ft2. Find the dimensions of the box with the largest possible volume if you are only allowed to spend Php 1440 for the material to make it