MATH 221 - Calculus I – Test #2 Name________________
Instructions:
Answer all the questions on the paper provided and show all your work. Clearly label your answers.
1. Find all the critical points (there may not be any) of f(x). Briefly explain why they are critical points. (18)
a)
b)
2.
Let
(18)
a)
Find
the intervals on which f(x) is increasing and is decreasing.
b)
Find
all local maximum and minimum points of f(x).
c)
Find
all points of inflection of f(x).
3.
Verify
the Mean Value Theorem for 
on the interval
[0,9]. (14)
4.
A
particle moves along the graph of 
in such a way that 
units per
second. Find 
when the particle
passes through the point (-1,1).
(16)
5.
Below
is the graph of f(x). In the blank
graphical region sketch the graph of 
.
(14)
