Page 62 - How To Solve Word Problems In Calculus

Solution
Step1

20 y

x

Step2
dx
Given: = 1 ← Since x is increasing, dx/dt is posi-
dt tive, even though the foot of the
ladder is moving to the left.
dy
Find: when x = 12
dt
Step3
Observing a right triangle, we use the theorem of
Pythagoras to obtain a relationship between x and y:

2
2
x + y = 20 2

Step4
Differentiate with respect to t:

d 2 d 2 d
x + y = 400
dt dt dt
dx dy
2x + 2y = 0 ← Divide by 2 for convenience
dt dt
dx dy
x + y = 0
dt dt

Step5
We know from step 2 that dx/dt = 1 and we know that
x = 12 at the instant in question. Before we can compute
dy/dt, however, we need to find y at this instant. This is

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