Question:

(A) 1 (B) 1.25 (c) 1.5 (D) 1.75 (E) 2 4 (C). On the interval [0,15] the number 0 = 0.7868 is the number guaranteed by the Mean Value Theorem for the function f (x) = cos )6. What is the approximate value of b? 5 (NC). Letf (x) : 25in2 x + 23in x . What are all real numbers 6 on the open interval (37%,?) SUCh thatf'(c) = 0? 7 11 (A 313.535 (3)1717\" (C 3411,47 2 2 2 2 6 6 5311x197: 3 D- E,, ()2'6'6 ()2 2 6 l E l E E 6 (C). For f (x) = cos x the Mean Value Theorem shows a tangent at point a = 2.751 will be parallel to a line drawn through the endpoints of the graph on the interval [0,b]. What is the approximate value of b? A) 4.111 x_ _:;Ma,thboatoo~mz Mathbout.com 3.3 First derivative test and graphing NC1. The function f (x) = x4 -4x2 has ( A) 1 relative minimum, 2 relative maximum 62 (B) 1 relative minimum, 1 relative maximum (C) 2 relative maximum, no relative minimum (D) 2 relative minimum, no relative maximum (E) 2 relative minimum, 1 relative maximum NC2. If the function f (x) =1-3x3 has an extremum, which of the following is the x coordinate of the extremum? Specify whether it is a maximum or minimum, or state if it doesn't exist. (A) x = 0, maximum (B) x=0, minimum (C) x=3, maximum (D) x= 3, minimum (E) No extrema exist NC3. For which of the following x coordinates does the function y = - x4 - 2x3 +7 have an extremum ? Specify whether it is a maximum or a minimum. (A) Max at x = 6, min at x = 0 (B) Max at x = 0, min at x = 6 C) Max at x = 0 (D) Max at x = 6 E) Min at x = 6 32NC4. At What value(s) of x does f (x) = x4 8x2 have a relative maximum? (A) 0 and 2 only (B) 0 and 2 only (C) 0 only (D) 2 and 2 only ( ) E 2, O,and2 C5. Let f be a mction Whose derivative is given by f '(x) = 12; + sin (elm). How many relative maximum points does f (x) have in the interval 0 S x S 12? (A) None (B) One (C) Two (D) Three (E) More than three @ " Mathboat.com NC6. How many extrema (minima and maxima) does the function f (x) =(x+1)" (x-2)' have on the open interval (-9,5)? (A) None (B) One (C) Two (D) Three (E) Four NC7. What is the absolute minimum of the function f (x) =4x' - x2 +3 on the interval [-3,6]? (A)-114 (B) O (C) 323 108 (D) -3 (E)