 
Summary: Math 1550 Fall 2005
Section 31 P. Achar
Exam 4 Solutions
November 17, 2005
Total points: 50 Time limit: 1 hour
No calculators, books, notes, or other aids are permitted. You must show your work and justify your
steps to receive full credit.
1. (5 points) Short answer:
(a) State the definition of critical point.
Solution: a point where the derivative is 0 or undefined
(b) Suppose f (3) = 0 and f (3) = 2. According to the second derivative test, what can you say
about f(x) at x = 3?
Solution: The second derivative test says that f(x) has a local minimum at x = 3.
(c) True or false: If f (4) = 0, then f(x) must have either a maximum or a minimum at x = 4.
Solution: FALSE. For example, the function f(x) = (x  4)3
has the property that f (4) = 0, but
it has neither a local minimum nor a local maximum at x = 4.
2. (5 points) Evaluate the following limit:
lim
x
