Question

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

Answer 1

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