Question

A rectangle has width w inches and height h, where the width is twice the height. Both w and h are functions of time,t, measured in seconds. If A represents the area of the rectangle, what is the rate of change of A with respect to t at the instant where the width is 4 inches and the height is increasing at the rate of 2 inches per second?

Answer 1

width = twice height
w = 2h or h = w/2

area = wh = 2h^2
A = 2h^2
dA/dt = 4h dh/dt
for the given data ... when w = 4, h = 2
dA/dt = 4(2)(2) inches^2 /sec
= 16 inches^2/sec