Page 67 - How To Solve Word Problems In Calculus

Step4
dx dy
2x + 2y = 0
dt dt

dx dy
x + y = 0
dt dt

Step5
dy
3 · 2 + 4 = 0 Since dx/dt is positive and the point is in the
dt first quadrant, the point is moving along the
circle in a clockwise direction. It makes sense
dy 3 that dy/dt is negative, as the point is moving
=− cm/sec down.
dt 2

EXAMPLE 8

The dimensions of a rectangle are continuously changing. The
width increases at the rate of 3 in/sec while the length de-
creases at the rate of 2 in/sec. At one instant the rectangle is a
20-inch square. How fast is its area changing 3 seconds later?
Is the area increasing or decreasing?

Solution
Step1
Represent the width and length of the rectangle by x and
y, respectively.
x

y

Step2
dx dy dA
Given: = 3, =−2 Find: 3 seconds later
dt dt dt
54