Page 224 - How To Solve Word Problems In Calculus

Step 5
Substitute all given information into the result of step
4 and solve for the unknown rate. Insert appropriate
units.

EXAMPLE 8
The cost C(x), in thousands of dollars, of a full-page advertise-
ment in a magazine is related to its monthly circulation by the
√
2
function C(x) = 5 x − 900. We assume x ≥ 30, where x is the
circulation in thousands of copies sold. If the circulation is
increasing at the rate of 3000 copies per month, how fast
is the cost of advertising increasing when 50,000 copies are
being sold?

Solution
Step 1
x = circulation (thousands of copies)

C = cost (thousands of dollars)

Step 2
dx dC
Given: = 3 Find: when x = 50
dt dt

Step 3

2
C = 5 x − 900
2
= 5(x − 900) 1/2
Step 4
dC dC dx
= ·
dt dx dt
dC 5 2 −1/2 dx
= (x − 900) (2x)
dt 2 dt
5x dx
= √
x − 900 dt
2

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