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.