How does optimization in Calculus work? A cylindrical can is made so that the sum of its height and its base is 45pi cm. Find the maximum possible volume of the can.

Question

How does optimization in Calculus work?  A cylindrical can is made so that the sum of its height and its base is 45pi cm.  Find the maximum possible volume of the can.

mathstudent55 · Answer

Find a formula or equation for what you want to optimize in terms of a variable. Then differentiate the equation with respect to that variable and set the derivative equal to zero. Solve the equation. That will give you the value of the variable at a maximum or minumum point of the equation.