Page 126 - How To Solve Word Problems In Calculus

2
2
x + y = 25
2
y = 25 − x 2
√
y = 25 − x 2
The area can now be expressed as a function of x. From the
diagram it is clear that 0 ≤ x ≤ 5.
√
A(x) = 2x 25 − x 2
2 1/2
= 2x(25 − x )
1
2 1/2
2 −1/2
A (x) = 2x · (25 − x ) (−2x) + 2(25 − x )

2
−2x 2
0 = √ + 2 25 − x 2
25 − x 2
2x 2 √
√ = 2 25 − x 2
25 − x 2
2
2
2x = 2(25 − x )
2
x = 25 − x 2
2
2x = 25
25
2
x =
2
5
x = √
2
Since A(0) = A(5) = 0, the maximum area is

5 10 25 10 25
A √ =√ 25 − = √ = 25 square inches.
2 2 2 2 2
6. Let x represent the side of the square cutout.

x x
x x

12"
x x
x x

12"
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