calculus problems

You may attach your work to the end of the uploaded document. Please keep the pages in order and turn in a printed copy of this test (do not do this test on your own paper).

Please write on this test.

1) For f (x) x3 x2 3x 4 find the following and then sketch the graph.

Domain _________________

First Derivative _________________

Increasing Intervals _________________

Decreasing Intervals _________________

Relative Max _________________

Relative Min _________________

Second Derivative _________________

Concave Down Intervals ______________

Concave Up Intervals _________________

Points of Inflection _________________

2) For f (x) cos2 x 2sin x, 0 x 2 , find the following and then sketch the graph

Domain _________________

First Derivative _________________

Increasing Intervals _________________

Decreasing Intervals _________________

Relative Max _________________

Relative Min _________________

Second Derivative _________________

Concave Down Intervals ______________

Concave Up Intervals _________________

Points of Inflection _________________

3) For the rational function f (x) = complete the following information and sketch the

graph.

Domain _________________

First Derivative _________________

Increasing Intervals _________________

Decreasing Intervals _________________

Relative Max _________________

Relative Min _________________

Second Derivative _________________

Concave Down Intervals ______________

Concave Up Intervals _________________

Points of Inflection _________________

Show all work to receive credit.

4. A ladder 7 m long is leaning against a wall. If the bottom of the ladder is pushed horizontally toward the wall at 1.5 m/sec, how fast is the top of the ladder sliding up the wall when the bottom is 2 m from the wall?

5. Oil is running into an inverted conical tank at the rate of 3 m3 per minute. If the tank has a radius of 2.5 m at the top and a depth of 10 m, how fast if the depth of the oil changing when it is 8 m high?

Extra Credit: (Worth 5 points). A spherical snowball is being made so that its volume is increasing at the rate of 8 ft3 min. Find the rate at which the radius is increasing when the snowball is 4 ft in diameter?