MATH 221 Review Exercises for Test 2

1. Find the equation for the tangent line to the graph of at (1,1).

2. Find all the critical points of the following functions and briefly state why they are critical points.

a)

b)

c)

3. Verify the Mean Value Theorem for over [1,4].

4. Find the intervals on which f(x) is increasing, and on which f(x) is decreasing.

5. Find the local maximum and minimum points for each of the following functions:

a)

b)

6. Find the intervals on which is concave upwards and is concave downwards, and find the points of inflection.

7. Find the linearization of f(x) = x³ – 6x at x = 3.

8. . Let f(x) be a function which is continuous on , has critical points at x = -2, x = 1, x = 5. The following values of the derivative are known:

Find all the local maximum and minimum points of f(x).

9. A farmer has 800 feet of fencing and wishes to construct a pasture as pictured below. Find the maximum area of such a pasture.