Consider the function f (@) = 2 - 9x + 5. Which of the following describes its local minima and maxima? O A. local minimum at x = -3; local maximum at x = 3 O B. local minimum at x = 3; local maximum at x = -3 O C. local minimum at x = -V3; local maximum at x = V3 O D. local minimum at a = V3; local maximum atx = - V3 O E. local minimum at x = -37; local maximum at x = 3iConsider the function f (x) = - + 6x2 -11x + 6. Which of the following describes the intervals over which it is increasing and the intervals over which it is decreasing? O A. increasing on (-0o, 2 - U 2+ , 00; decreasing on 2 - 3 2 + 3 B. decreasing on (-oo, 2 - ; ] u [2 4 , 00) ; increasing on [2 - 27, 2 3 C. increasing on (-00, -2, |U 2, 00 ) ; decreasing on 2V/3 2V/3 9 9 O D. decreasing on (-oo, - |U , co ); increasing on 2V/3 2V/3 9 9 O E. increasing on (-oo, 1] U [2, 3]; decreasing on [1, 2] U [3, co)Coneioerthe function f [53} = 3:1:2 2:1: 1. What does the Mean Value Theorem guarantee about this function over the interval [1, 3]\"? O A. that 3'{:E} is continuous over the interval [1, 3] O E. that an x exists in the interval [1, 3] such that f' (it) = 21] O C. that an x exists in the interval [1, 3] such that f' (it) = 11] O D. that an xexiete in the interval [[1, 21]] such that j\" [53} 2 2B O E. that an xexiete in the interval [[1, 21]] such that j\" [33} = 13 The graph of y = sin x - cost is concave up on which of the following intervals? O A. (- 4 O B. (-7, 0) O C. (0, TT) O D. 4 " 4 O E. 4 4Find the function whose derivative is f (@) = 4x -7 and whose graph passes through the point (2, -7) O A. f(x) = 4 O B. f(x) = 4x - 13 O c. f(x) = 2x2 - 7x O D. f(x) = 4x2 -7x-7 O E. f(x) = 2x2 -7x - 1Use the derivative f' (x) = (x - 1) (x - 2)' to identify the inflection points of the function f (). O A. x = 2 O B. T= O CE= and x = 2 O D. X = 1 O E. f (a) has no inflection points.Use the second derivative test for local extrema to determine the maxima and minima for f (x) = 23 -5x- + 3x - 1. O A. local maximum: = local minimum: x = 3 O B. local maximum: > = 3, no local minimum O C. local maximum: none; local minimum: x = 09 0 O D. local maximum: x = 3; local minimum: > = 09|K O E. local maximum: x ~ 4.3652; no local minimumA chemical refinery needs a vat. They want the vat to be a rectangular prism (with square bases) that has a maximum volume of 1,000 cubic feet. They want to have it constructed to use the least amount of material. What should the lengths of the bases and sides be? (Note: One of the bases is the lid.) O A. 10 ft. for the base and sides O B. 10 ft. for the base and 100 ft. for the sides O C. 100 ft. for the base and 10 ft. for the sides O D. 33.3 ft. for the base and 33.3 ft. for the sides O E. 50 ft. for the base and 10 ft. for the sidesFind the paint an the graph of f (3:) : J57: that minimizes the distance between [4, U] and the paint an the graph. In ether wards: find the paint an the graph of f (at) that is closest to (4, 1]). O a. (4,2) 0 a. (17151?) O C- (as) O D. (13 g) Q E. (EH/E) Determine the first three iterations of one of the zeros of the function f (x) = 3x - 16x2 -32x - 10 using Newton's Method. Begin with 0 = -1.5. Round each iteration to the thousandths place before finding the next iteration. O A. 1 = -1.346, x2 = -0.871, x3 = -0.397 O B. x1 = -1.209, x2 = -0.397, 3 = 6.940 O C. *1 = -1.724, x2 = -2.080, x3 = -2.620 O D. x1 = -1.276, x2 = -1.214, x3 = -1.209 O E. x1 = -1.500, x2 = -1.276, x3 = -1.2142 The circumference C and area A of a circle are related by the equation A = Which of the following equations relates dA dt to dt O A. d.A C dC dt dt O B. dA C dC dt dt O C. d.A dC dt IT dt O D. dA dC dt dt OE. d.A = C do dtA woman who is 6 feet tall walks at a rate of 4 ft./sec toward a streetlight that is 15 ft. above the ground. At what rate is the length of her shadow changing when she is 22 ft. from the base of the light? (Round to the nearest 0.01 ft./sec. if necessary.) O A. -2.67 ft. /sec. O B. -1.60 ft. /sec. O C. -1.14 ft./sec. O D. 1.14 ft./sec. O E. 2.67 ft. /sec