y = (cosx) raise to 3

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

Optimization Problem: A rectangle has a perimeter of 80 cm. If it's width is x, express it's length and area in terms of x, and find the maximum area.

A rectangle has a perimeter of 80 cm. If it's width is x, express it's length and area in terms of x, and find the maximum area.

Optimization Problem: A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?

A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?

The combined perimeter of an equilateral of a triangle and square is 10. Find the dimensions of the triangle and square that produce a minimum total area.

Suppose you had 103 m of fencing to make two side-by-side enclosures. What is the maximum area that you could enclose?

y = cos 2x (e^x2-1)

A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12m of framing materials what must the dimensions of the window be to let in the most ligh?

differentiate

A rectangular piece of paper is 12 inches high and 6 inches wide. the lower right-hand corner is folded over so as to reach the leftmost edge of the paper. find the minimum length of the resulting crease.

Construct a window in the shape of a semi-circle over a rectangle. If the distance around the outside of the window is 12 feet, what dimensions will result in the rectangle having largest possible area ?

DERIVATIVE

Find the derivative of y = 3 sin³ (2x⁴ + 1)

A rectangular pen will be built using 100 feet of fencing. What dimensions will maximize the area?

g(x)=x csc x/3-csc x

Derivation

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

y=x^3 tan x

Build a rectangular pen with 3 parallel partitions using 500 feet of fencing. What dimensions will mazimize the total area of the pen?

y=e^3lnx(2x+1)

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?