The function f(x) has a relative ? at this point. (D, E) (E, 0.) The second relative extremum (from the left) for f(x) occurs For each of the following intervals, classify whether th at x = graph of y = f(x) is CU or CD over that interval (short for con- The function f(x) has a relative ? at this point. cave up or concave down). (-00, A) The third relative extremum (from the left) for f(x) occurs (A, B) at x = (B, C) The function f(x) has a relative |? at this point. (C, D (D, E) The first inflection point (from the left) for f(x) occurs at x = (E, 00 Answer(s) submitted: The second inflection point (from the left) for f (x) occurs at x = . Answer(s) submitted: (incorrect) 5. (1 point) The picture below shows the graph y = f'(x) of the derivative of a function y = f(x). (incorrect) 6. (1 point) Use Newton's method to find the second and third approximation of a root of x+x+3=0 starting with x1 = -1 as the initial approximation. The second approximation is x2 = The third approximation is x3 = For each of the labelled points on the graph, classify the corre- Answer(s) submitted: sponding point on the graph of y = f(x) as on of the following: MAX, MIN, INFL, INT (short for maximum, minimum, inflec- tion point, x-intercept) (incorrect) A: 7. (1 point) B: C: Use Newton's Method with the function f(x) =x3 -5 and initial D: value xo = 1.6 to calculate x1, X2,X3. B: X1 = For each of the following intervals, classify whether the X2 = graph of y = f(x) is INC or DEC over that interval (short for X3 =_ increasing or decreasing). Answer(s) submitted: (-0o, A) (A, B) (B, C (C, D) (incorrect). F. I 1. (1 point) . G. S On what intervals is the function f(x) = x8 - 8x7 both de- . H. t creasing and concave up? Check the boxes of the points where the graph has an global interval(s) = minimum Give your answer as an interval or a list of intervals, e.g., (- infinity,8] or (1,5),(7,10) .) Answer(s) submitted: . A. a . B. b . C. c (incorrect) . D. d 2. (1 point) . E. e Consider the function f(x) graphed below. . F.r . G. S . H. t Check the boxes of the points where the graph has a local maximum . A. a . B. b . C. c . D. d . E. e . F.r For this function, are the following nonzero quantities posi- . G. S tive or negative? . H. t f(4) is [?/positiveegative] Check the boxes of the points where the graph has a local f' (4) is [?/positiveegative] minimum f" (4) is [?/positiveegative] (Because this is a multiple choice problem, it will not show A. a which parts of the problem are correct or incorrect when you B. b submit it.) . C. c Answer(s) submitted: . D. d . E. e . F. I . G. S (incorrect) H. t 3. (1 point) Answer(s) submitted: Check the boxes of the points where the graph has an global maximum (incorrect) 4. (1 point) Suppose that it is given to you that . A. a . B. b f'(x) = (x+7)(10-x)(x-17) . C. C . D. d Then the first relative extremum (from the left) for f(x) occurs . E. e at x =