Find two nonnegative number whose sum is 9 and so that the product of one number and the square of the other number is a maximum.

Test your skill!

Find the derivative of the given function

Solution

Optimization: Find Out!

A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction.

Solution

DERIVATIVES

Differentiate y = 4 cos (6x² + 5)

OPTIMIZATION

There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees?

A container in a shape of a right circular cylinder with no top has a surface area of 3π sq ft. What height h and base radius r will maximize the volume of the cylinder?

Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total are of the pen?