MATH 2431 – Summer Session 2005

TEST 4

NAME_______________________________________________________

You may NOT use a calculator on this portion of the test. Show work and write clearly.

1. (20 points) At a given instant the legs of a right triangle are 5 cm and 12 cm long. If the short leg is increasing at the rate of 1 cm/sec and the area is decreasing at the rate of 2 cm²/sec, how fast is the long leg changing?

2. (20 points) Evaluate the following limits:

a.

b.

c.

3. (12 points) The cost of producing x units of a commodity is given by .

a. Find the marginal cost function.

b. Find the minimum value of the marginal cost.

4. (12 points) Find intervals of concavity: .

5. (12 points) Find the global (absolute) maximum and the global (absolute) minimum of on [–1, 3]. Explain (in detail) how you know there is a global maximum and a global minimum.

6. (12 points) Given

a. Find the critical numbers of f(x).

b. Find the intervals of increase/decrease of f(x).

7. (12 points) The graphs of and are provided below. Find:

a. approximate critical numbers and inflection points of . Explain.

b. approximate intervals of increase/decrease for . Explain.

c. approximate intervals of concavity for . Explain.

d. approximate maximum and minimum points of . Explain.