Page 95 - How To Solve Word Problems In Calculus

Step4
Using the chain rule,

A (y) = 2(6 − 2y)(−2) + 6y

=−24 + 8y + 6y
=−24 + 14y

0 =−24 + 14y
24 12
y = =
14 7

Step5
Compute A(y) at the critical numbers and at the end-
points of the interval.

2
A(y) = (6 − 2y) + 3y 2
A(0) = 36 ← All the wire is used to form the
square.
2 2
12 24 12
A = 6 − + 3
7 7 7
2 2
18 12
= + 3
7 7
324 432
= +
49 49

756 108
= = ≈ 15.43
49 7
A(3) = 27 ← All the wire is used to form the
rectangle.

The maximum area occurs at the left endpoint of the in-
terval, y = 0, when all the wire is used to form the square.
12
The minimum area occurs when y = . To minimize the
7
96 5
combined area, the wire should be cut 8y = = 13 inches
7 7
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