Chapter 3.4, Problem 5ES

Let $A$ be the area of a square whose sides have length $x$ , and assume that $x$ varies with the time $t$ .

(a) Draw a picture of the square with the labels $A$ and $x$ placed appropriately.

(b) Write an equation that relates $A$ and $x$ .

(c) Use the equation in part (b) to find an equation that relates $dA/dt$ and $dx/dt$ .

(d) At a certain instant the sides are $3\text{ ft}$ long and increasing at a rate of $2\text{ ft/min}$ . How fast is the area increasing at that instant?