For a given function f, what does f' represent? Choose the correct answer below. 0 A. f\" is the average rate of change of f. O B. f' is the tangent line function of f. O c. f\" is the difference quotient of f. O D. f' is the slope function of f. If f is differentiable at a, must f be continuous at a? . . . Choose the correct answer below. O A. No, if f is differentiable at a and positive at a, then f is continuous at a. O B. No, if f is differentiable at a and does not have a vertical tangent at a, then f is continuous at a. O C. No, if f is differentiable at a and does not have a corner at a, then f is continuous at a. O D. Yes, if f is differentiable at a, then f is continuous at a.If f is continuous at a, must f be differentiable at a? Next question . . . Choose the correct answer below. O A. Yes. If f is differentiable at a, then f is continuous at a. The contrapositive of this statement therefore states, if f is continuous at a, then f is differentiable at a. O B. No. If f is differentiable at a, then f is not continuous at a. The contrapositive of this statement therefore states, if f is continuous at a, then f is not differentiable at a. O C. No. If f is continuous at a, it is not necessarily true that the limit that defines f' exists at a. O D. Yes. If f is continuous at a, it is necessarily true that the limit that defines f' exists at a.Use the graph of f to sketch a graph of f'. Cho Next question ph off'. O A. 10 Ay O B. 10- 8- 10- 6- 1993 1998 -101 19950 1998 4- -101 O C. 2- OD. 10- 1993 1994 1995 1 102 1996 1997 1998 1993 1998 - 101 1993 1998Next question Use the graph of f in the figure to do the following. a. IN IS not continuous at x = a. Find the values of x in the interval (0,5) at which f is not continuous. (Use a comma to separate answers as needed.) b. Find the values of x in the interval (0,5) at which f is not differentiable. 10- X POPINONAEnergy is the capacity to do work, and power is the rate at which energy is used or consumed. Therefore, if E(t) is the 3. Estimate the power at t = 15 hr. Choose the correct answer below. energy function for a system, then P(t) = E'(t) is the power function. A unit of energy is the kilowatt-hour; the corresponding units for power are kilowatts. The graph shows the energy demand function for a small community over a 25 hr period Complete parts a through c O A. The power at t = 15 hr is approximately 403 kW. I I O B. The power at t = 15 hr is approximately -403 kW. E , 450 0' O C. The power at t = 15 hr is approximately 5 kw. Q O D. The power at t = 15 hr is approximately 5 kW. 400 E ' l3 5 350 . I 2' 2 300 HJ 250 200 > 0 5 10 15 20 25 1 Time (hrs) t c Next question Use the points A, B, C, D, and E in the graph to the right to answer the following questions. a. At which point(s) is the slope of the curve negative? b. At which point(s) is the slope of the curve positive? D c. Using A-E, list the slopes in decreasing order. A E B C a. Choose the correct answer below. O A. D, E O B. B, D, E OC. A, C O D. B, C, E_ t tion Sketch a graph of the derivative of the function f shown to the right. ex ques y=g(x) y Q ' Which graph below shows a sketch of the derivative of f? OA. Use the graph of g in the figure to do the following. a. In the interval ( - 4,4), g is not continuous at x =. a. Find the values of x in ( - 4,4) at which g is not continuous. (Use a comma to separate answers as needed.) b. Find the values of x in ( - 4,4) at which g is not differentiable. c. Sketch a graph of g'. 10 1y 10Create the graph of a continuous function f that has f'(x) given below. Is it possible to create more than one graph? -1 ifx 2 Choose the correct graph of f(x) below. O A. O B. O C. Ay OD. Ay Ay HIIN 10 40