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7 Feb 2018

(7) Let f(x) = (22 - 3)e". On which interval(s) is the function f decreasing? (A) (-13, 13) (B) (-20, -3) U (1,00) fla= 2x et +(13 = (x?+2x-3) = (x +3)(x-1) (©) (-3,1) (D) f is always increasing. (E) None of these.

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Lelia Lubowitz
Lelia LubowitzLv2
9 Feb 2018
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(5) Let g(x) = x2 +22/3. At which point(s) does the function have a local minimum? (B) 2 = 1. (C) = 0. g'KI= 2x+ g' ONE @ x=0 Fag=0 2x+ 20 (D) f has no local minimum. (E) None of these.

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

13. Suppose that f is a function such that for all x, f" () = (1 - 1)(x + 2)²(22 – 4)(x2 – 3x)(x2 - 9)?(22 – 42 + 3). How many points of inflection does the graph of f have? A five B two © four D three € more than five

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