Part I. Multiple Choice: Graphing Calculator Permitted 1. State a(some) reason(s) why the Rolle’s Theorem does not apply to the function on the interval [-3, 0]. a. is not defined at x = -3 and x = 0 b. is not continuous at x = -1.5 f f c. d. Both b and c. e. None of these. 2. The first derivative of the function f is given by . How many critical values does have f on the open interval ? a. One b. Three c. Four d. Five e. Seven 3. If , then there exists a number in the interval that satisfies the conclusion of c the Mean Theorem. Which of the following could be c? a. b. c. d. e. 4. The derivative of is . At how many points will the graph of have a relative maximum? f f a. None b. One c. Two d. Three e. Four 5. If , then the graph of f has inflection points when ? a. only b. 2 only c. and 0 only d. and 2 only e. , 0, and 2 only Part II. Free Response: Graphing Calculator Permitted 6. The figure below shows the graph of , the derivative of the function for . The graph of f, has horizontal tangent lines at , , and ,, and a vertical tangent at .
Part I. Multiple Choice: Graphing Calculator Permitted 1. State a(some) reason(s) why the Rolle’s Theorem does not apply to the function on the interval [-3, 0]. a. f is not defined at x = -3 and x = 0 b. f is not continuous at x = -1.5 c. d. Both b and c. e. None of these. 2. The first derivative of the function f is given by . How many critical values does f have on the open interval ? a. One b. Three c. Four d. Five e. Seven 3. If , then there exists a number c in the interval that satisfies the conclusion of the Mean Theorem. Which of the following could be c? a. b. c. d. e. 4. The derivative of f is . At how many points will the graph of f have a relative maximum? a. None b. One c. Two d. Three e. Four 5. If , then the graph of f has inflection points when ? a. only b. 2 only c. and 0 only d. and 2 only e. , 0, and 2 only Part II. Free Response: Graphing Calculator Permitted 6. The figure below shows the graph of , the derivative of the function f, for . The graph of has horizontal tangent lines at , , and ,, and a vertical tangent at .