MATH 221 Test 2 Part 1 Name_______________

Instructions: Find the derivative of each of the following functions. 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. Let . Find the absolute maximum and minimum points of f(x) over the interval [-1,4]. (20)

2. Using a linearization, estimate . (10)

3. Find the equation of the line tangent to the graph of at the point (2,1). (15)

4. Find all the critical points of the following functions: (15)

a)

b)

c)

5. Verify the Mean Value Theorem for over [-3,1]. (15)

6. Find the second derivative of . (5)