Chapter 12.5, Problem 18E

Changing pyramid The volume of a pyramid with a square base x units on a side and a height of h is $V=\frac{1}{3}{x}^{2}h$.

a.    Assume that x and h are functions of t. Find V’(t).

b.    Suppose that x = t/(t + 1) and h = 1/(t + 1),for t ≥ 0. Use part (a) to find V’(t).

c.    Does the volume of the pyramid in part (b) increase or decrease as t increases?