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Rates of Change

Maximization

Small Changes

Quiz

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Maximization & Minimization

Maximum and minimum values of a function can be found, like in a cartesian plane. The methods and finding, as well as that of testing the nature of the point, are the same.

A solid right cylinder is removed from a solid sphere of radius 10cm, as shown. If the height of the cylinder is 4x cm, show that the volume of the cylinder is V = 400px - 16px³. Find the maximum volume of the cylinder as x varies.

Solution:

             

             

              shown

                                 ^{reject negative answer as x > 0}

        when ,