1. Find the graph given the following table. Choose the correct graph. x f'x OA- a 0 Y b 0 c -8 2. Deten'nine all critical points for the tollowing function. f(x)=x2 -12x+3 x = (Use a comma to separate answers as needed.) a. f(b) - f(a) Find the value or values of c that satisfy the equation W =f '(c) in the conclusion of the mean value theorem for the given function and interval. f(x) = .l'x- 2, [2,8] (Simplify your answer. Use a comma to separate answers as needed.) 4- Answer the following questions about the function whose derivative is a. What are the critical points of t? given below. b. On what intervals is f increasing or decreasing? 1:. At what points, if any, does fassume local maximum and {'{x) = (x -1)2(x + 5) minimum values? a. What are the critical points of f? x = [: (Use a comma to separate answers as needed.) b. On what interval(s) is f increasing? Select the correct choice below and ll in any answer boxes in your choice. 0 A- The function is increasing on the interval(s) . (Type your answer in interval notation. Use a comma to separate answers as needed.) 0 B. There is no interval on which the function is increasing. On what intervai(s) is f decreasing? Select the correct choice below and ll in any answer boxes in your choice. 0 A- The function is decreasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) 0 B. There is no interval on which the function is decreasing. c.At what point(s), if any, does f assume a local maximum value? Select the correct choice below and ll in any answer boxes in your choice. 0 A- x = (Use a comma to separate answers as needed.) 0 B. There are no local maxima. At what point(s). it any. does fassume a local minimum value? Select the correct choice below and ll in any answer boxes in your choice. 0 A- x = (Use a comma to separate answers as needed.) O B. There are no local minima. 5. Identify the inflection points and local maxima and minima of the function. Identify the intervals on which the function is concave up and concave down. y= - 2x - sin 4x, Choose the correct list of inflection points below. O A. (-* 3). (0.0). (. -3) O c. (-2). (: -2) Choose the correct list of local maxima below. O A. O c. Choose the correct list of local minima below. O A. O C. Choose the correct interval(s) on which the function is concave up. OA (-0) (3) Oc. (-7.0) OF. (- 3 -# ) (23) Choose the correct interval(s) on which the function is concave down. O A. (-20) (#3) Oc. (-;-7) (3 OF. (- 3 -#) (0.#) 6. Find the coordinates of any local extreme points and inflection Choose the correct graph of y = x2 - 8x + 7. points. Use these to graph the function y = x - 8x + 7. Choose the correct answer regarding local extreme points. O A. O A. The function has a local minimum at (4, - 9). O B. The function has a local maximum at (4, - 9). O C. The function has no local extreme points. Choose the correct answer regarding inflection points. O c. O A. The function has no inflection points. O B. The function has an inflection point at (4, - 9). O C. The function has an inflection point at (0,7). O D. The function has inflection points at (7,0) and (1,0).7. Find the coordinates of any local extreme points and inflection Choose the correct graph of y = x - 3x + 4. points. Use these to graph the function y = x - 3x +4. O A. Choose the correct local extrema. O A. There is a local minimum at (- 1,6) and a local minimum at ( O B. There are no local extreme points. O C. There is a local maximum at ( - 1,6) and a local minimum at O D. There is a local minimum at (0,4). O C. Choose the correct inflection points. O A. There is an inflection point at (0,4). O B. There are inflection points at ( - 1,6) and (1,2). O C. There are no inflection points. . Consider the parabolic arch whose shape may be represented by the graph y = 196 - x", where the base of the arch lies on the x-axis from x = - 14 to x = 14. Find the dimensions of the rectagular window of maximum area that can be constructed inside the arch. The width of the rectangular window is The height of the rectangular window is (Type exact answers, using radicals as needed.) 9. Find the antiderivative for each function when C equals 0. Check your answers by differentiation. (a) g(x) = - 6x7 (b) h(x) =x" (c) k(x ) = x +3x2 +4 (a) G(x) = (b) H(x) = (c) K(x) = 10. Find the antiderivative of the function f(x) = - 7 sin (7x) when C = 0. The antiderivative is