Page 66 - How To Solve Word Problems In Calculus

2
2
z = x + 2 2
= 64 + 4
= 68
√ √
z = 68 = 2 17

From step 4,

√ dz
2 17 = 8 · 480
dt
dz 1920
= √ mi/h
dt 17

EXAMPLE 7
2
2
A point is moving along the circle x + y = 25 in the first
quadrant in such a way that its x coordinate changes at the
rate of 2 cm/sec. How fast is its y coordinate changing as the
point passes through (3, 4)?

Solution
Step1

5
(x, y)

−5 5

−5

Step2
dx dy
Given: = 2 Find: when x = 3 and y = 4
dt dt
Step3
Since the point must lie on the circle, the relationship
2
2
between x and y is x + y = 25.
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