Page 91 - How To Solve Word Problems In Calculus

Step4
2
Since A(x) = 50x − x is a polynomial, its derivative exists

everywhere. The critical values occur where A (x) = 0.
A(x) = 50x − x 2

A (x) = 50 − 2x = 0
x = 25

Step5
We use the closed interval method.

x A(x)

0 0
25 625
50 0

2
The maximum area is 625 ft .
EXAMPLE 3
What is the minimum possible perimeter for a rectangle whose
2
area is 100 in ?
Solution
At first glance this problem appears similar to Example 2.
We shall see, however, that it is somewhat different and must
be solved using another strategy.

Step1

y

x

Step2
We wish to minimize the perimeter.

P = 2x + 2y

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