Page 68 - How To Solve Word Problems In Calculus

Step3
A = xy
Step4
dA
We use the product rule to compute . All derivatives
dt
are taken with respect to t.

dA dy dx
= x + y
dt dt dt

Step5
3 seconds later, x = 20 +3·3 = 29 and y = 20 + 3(−2) = 14
dA
= 29 · (−2) + 14 · 3 =−16
dt

dA
Since is negative, the area is decreasing at the rate of
dt
2
16 in /sec.
EXAMPLE 9
A trough filled with water is 2 m long and has a cross section in
the shape of an isosceles trapezoid 30 cm wide at the bottom,
60 cm wide at the top, and a height of 50 cm. If the trough
3
leaks water at the rate of 2000 cm /min, how fast is the water
level falling when the water is 20 cm deep?
Solution
Step1

60 cm

2 m
50 cm x cm
h
30 cm
55