MATH 221 Test 2 Fall 2000 (Part1) Name______________

Instructions: Answer all the questions on the paper provided and show all your work so that partial credit may be given. Make sure that your solutions to the problems are clearly indicated. You may use a calculator for all problems on this test.

1. Find all the critical points of the following functions. (15)

a)

b)

c)

2. Determine the intervals on which is increasing and on which it is decreasing. (10)

3. Determine the intervals on which the graph of is concave upwards and concave downwards. Find the points of inflection. (15)

4. Let f(x) be a function which is continuous on , has critical points at x = -2, x = 1, x = 5. The following values of the derivative are known:

Find all the local maximum and minimum points of f(x). (10)

5. Verify the Mean Value Theorem for on the closed interval [1,4]. The theorem essentially states that the slope of a certain tangent line equals the slope of a certain secant line. Find the equations of those two lines. (15)

6. a) Find all the points on the graph of at which the tangent lines are horizontal. (5)

b) Find all the points on the graph of at which the derivative is undefined. (5)