whereas Problems 2 and 3 are about determining this information algebraically. A hint for Problem 1: remember that there are two "flavors" of critical points. . The graph of the derivative f'of a continuous function f is shown. Use the graph to determine the following. For each, give a very short description (i.e. a few words) indicating how you found them. a. critical points of f. ( notice f, not f ') y y = f(x), b. intervals where f is decreasing. 2 C. values of x where f has a local maximum. 6. d. values of x where f has a local minimum. -2 e. intervals where f concave down. f. values of x where f has an inflection point g. Assuming that f(0) = 0, sketch a graph of f using the axes given. (Recall that f is continuous.) +2 -1 5. 6. 10

For the followings problems, consider a function h that is twice differentiable. This means that his differentiable and its derivative, h', is also differentiable. Some values of h' (x) are given in the table below: Determine all intervals in which h must have an inflection point. (-8,-4) □ (-4,0) (0,4) (2,6) (4,8) (-8,-6) (-4,-2) (-2, 0) (2,4) (6,8) x -8 -6 -4 -2 0 2 4 h'(x) 3 7 0 -3 -5 -4 0 Determine all intervals which contain a number c satisfying h" (c) = 2. 0-2 6 8 -2 6 Suppose that h" (x) < 0 for a <-8, and h(-8)= 7. Select all numbers that could be reasonable values of h(-10). 0-1 00 01 02

The following graph is the graph of a function f. Use the graph off to sketch the graph of its derivative,f′. ( Make sure to clearly label the units on your axes) Make sure to use open circles to graph any points where the derivative is undefined.