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)