91Ó°ÊÓ

Explain why the function \(f(x)=1 / x\) has no local maxima or minima.

A container holding a fixed volume is being made in the shape of a cylinder with a hemispherical top. (The hemispherical top has the same radius as the cylinder.) Find the ratio of height to radius of the cylinder which minimizes the cost of the container if \((\) a) the cost per unit area of the top is twice as great as the cost per unit area of the side, and the container is made with no bottom; \((b)\) the same as in \((a),\) except that the container is made with a circular bottom, for which the cost per unit area is 1.5 times the cost per unit area of the side.