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The sum of radius and height of a conical tank is 60 inches. Find the radius and height of maximum volume. What is the exact maximum volume using these conditions? Volume of cone is V=1/3pir^2h

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Maximization by using derivatives

Given a function f(x), we can find the values of x that make f a maximum or a minimum by using derivatives.

Let f'(x) be the first derivative of f(x) and f''(x) the second derivative of f(x)

If f'(a) = 0 and f''(a) is negative, then x=a is a maximum

We'll use that criteria to find the maximum volume of the conical tank, restricted by the condition that the sum of radius and the height is 60 inches

User Paul Straw
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