# Optimization

A wire 10 feet long is to be cut into two pieces, each of which is to formed into a square. What is the largest possible total area of the two squares? What is the smallest possible total area?

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#### Solution Preview

Let 2 pieces be x , 10-x.

Total Area = x^2 + (10-x)^2

A = X^2 + 100 + X^2 -20X

dA/dx = 4x - 20.

d2A/d2x ( second derivative) ...

#### Solution Summary

The optimization for the total areas of squares are given. The smallest possible total area are analyzed.

$2.19