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.