1 Maximize

B=3xy2,

where x and y are positive numbers such that

x+y2=1.

The maximum value of B is

2

A rectangular box with a volume of 1088 ft3 is to be constructed with a square base and top. The cost per square foot for the bottom is 20, for the top is 15, and for the sides is 2.5. What dimensions will minimize the cost?

What are the dimensions of the box?

The length of one side of the base is

The height of the box is

3. Let

f(x)=3xraise to power 2.

a) Find the linearization L(x) of f at

a=2.

b) Use the linearization to approximate

3(2.1) raise to power 2

c) Find

3(2.1) raise to power 2

using a calculator.

d) What is the difference between the approximation and the actual value of

3(2.1) raise to power 2.