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24 Dec 2017

24 4(3-1) [7] 6. Let f(x) = 12 6- (In 3)2 + 10%(x+1)2 ( 9 + log(x+1)2(x + 1)2014 be a function defined on the interval (0,0). Show that the graph of f(x) on the interval (0,0) has an inflection point.

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Keith Leannon
Keith LeannonLv2
24 Dec 2017
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48 f(x) = 12 + (x + 1)2 4. (22 pts) The function f, its derivative f', and its second derivative f" are given by the expressions below. f'(x) = -96(x+1) (12+(x + 1)2) (12+(x + 1)2) (a) Circle the correct statement. f"(x)288(x2 + 2x - 3) i. f is even ii. f is odd. iii. f is neither even nor odd. (b) Give an equation for each horizontal asymptote of f. Write "none" if appropriate. Show your work. Show work for parts (c), (d), (e), and (f) in the space below. (c) List the interval(s) on which f is increasing. Write "none" if appropriate. (d) List the interval(s) on which f is decreasing. Write "none" if appropriate (e) List the x-value(s) at which the local minima of f occur. Write "none" if appropriate (f) List the x-value(s) at which the local maxima of f occur. Write "none" if appropriate. (8) List the interval(s) on which f is concave up. Write "none" if appropriate. (h) List the interval(s) on which f is concave down. Write "none" if appropriate. (i) List the x-coordinate(s) of the inflection points of f. Write "none" if appropriate. () Sketch the graph of y = f(x). Mark the locations of any local extrema and/or inflection points with filled-in circles. Your sketch should be consistent with your answers to (a)-0). -10 -9 -8 -7 -6 -5 -4 4 5 6 7 8 9 10

6. (14 pts) EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN. The graph of f'(derivative of f) on the interval [-6, 7] is shown in the figure. y f(x) y = f'(x) -6 -5 -4 -3 2 L - 2 3 4 5 7 Use the given graph of f' to answer the following questions about f: (a) (2 pts) on what interval (or intervals) is f decreasing? (b) (3 pts) Find the critical points of f. (c) (2 pts) which critical points (or point) correspond to local maxima ? (d) (2 pts) which critical points (or point) correspond to neither local maxima nor local minima ? (e) (2 pts) on what interval (or intervals) is f concave up? (f) (3 pts) At what point (or points) does f have an inflection point ?

1. (16 pts) Let f be the function with domain [0, 6] given by the graph below. y=f(x) 3 4 5 6 Use the graph off to answer the following questions about f. (a) List the critical point(s) of f on the interval (0,6). Write "none" if appropriate. (b) List the inflection point(s) of f on the interval (0,6). Write "none" if appropriate. Use the graph off to answer the following questions about the derivative f' of f. (c) List the intervals(s) on which f' is negative. Write "none" if appropriate. (d) List the intervals(s) on which f' is decreasing. Write "none" if appropriate. (e) List the x-coordinates(s) at which f' has a local minimum. Write "none" if appropriate.

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