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5-40.

Notice that the rectangle is symmetric across the y-axis.

Because of the symmetry, the endpoints of the rectangle can be found at −x and +x... after all, the distance between −x and x is 2x, the length of the base.

Consequently, the height of the rectangle can be evaluated at f(x):
height = y = −x2 + 5

Area = (base)(height)
Use the base and height you found in part (a).Then optimize the Area function.

To find the maximum Area:
1. Let A'(x) = 0.
2. Solve for x.
3. Use the x and your expressions for base & height to calculate the maximum area.

A cylinder with height __________ and radius __________.

Volume of a cylinder: V = πr2h
If you need guidance optimizing the volume, refer to steps in part (b).