Math 241

The graph of the derivative of the function f is shown. Determine the x-coordinates of all stationary and singular points of f, and classify each as a relative maximum, relative minimum, or neither, if a = 7 and b = 2. (Assume that f(x) is defined and continuous everywhere in  HINT [See Example 5.]

f has a singular     at x =    minimum at x =        at  x = 0.

[removed] [removed] [removed]

Solve the optimization problem. HINT [See Example 2.]P = [removed]

[removed][removed]

For a rectangle with a perimeter 56 to have the largest area, what dimensions should it have? (Enter the smaller value first.)
[removed] × [removed]

[removed][removed]

Assume that it costs Apple approximatelydollars to manufacture x 30-gigabyte video iPods in a day.† How many iPods should be manufactured in order to minimize average cost?
[removed] iPods per day

What is the resulting average cost of an iPod? (Give your answer to the nearest dollar.) HINT [See Example 1.]
$ [removed]

[removed][removed]

I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $144 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose? HINT [See Example 2.]

north and south sides	[removed] ft
east and west sides