MATH 221 Test 2 Name______________
Instructions: Clearly indicate your answers to the following questions. You may use a calculator on this test for all questions.
1. Find all the critical points of the following functions and briefly indicate why they are critical points. (15)
a) 
b) 
c) 
2. A rectangular poster has an area of 320 square inches. The rectangular printed area has margins of 2” on the sides and the bottom and a margin of 3” along the top. What dimensions of the poster give the maximum printed area? (20)
3. Find the
linearization of 
at x = 3. (10)
4. Find the equation
of the tangent line to the graph of 
at (1,-1). (10)
5. The critical points of 
are -2, 0, and 2. Which of these critical points are local
maximum points and which are local minimum points? (10)
6. Find the intervals
on which 
is increasing,
decreasing, concave up, and concave down. (15)
7. Below is the graph of the derivative of a function f(x). Using the graph determine the critical points of f(x), the inflection points of f(x), and the local maximum and minimum points of f(x). (20)
