MATH 221 Test 2 Part 1 Name_______________

Instructions: Find for each of the following. You may not use a calculator on this part. (20)

1. 1.________________

2. 2.________________

3. 3.________________

4. 4.________________

MATH 221 Test 2 Part 2 Name________________

Instructions: Answer all the questions on this part. You may use a calculator foa all questions on this part. Show all your work so that partial credit may be given.

1. A rectangular poster has 50 square inches of printed material with margins of 2 inches on the sides, 3 inches on the bottom, and 5 inches on the top. What is the minimum possible area of the whole poster? (20)

2. Find the linearization of at x = -2. (10)

3. Find the intervals of concavity for the function f(x) = 6x⁵ – 20x³. (10)

4. Find and classify all the critical points of the following functions: (21)

a)

b)

c)

5. Verify the Mean Value Theorem for over [1,4]. (12)

6. Give an example of a function, f(x), (by formula) such that f(x) has a critical point at

x = 0 but does not exist. (7)