8. [10 points] Let f() = 21/3 (2 – 2). (a) Find the critical points of y = f(), determine the intervals of increase and decrease and find relative extrema. (A sign chart is required.) (b) Explain if it is possible to find absolute extrema for y = f(x) on (-1, 4]. Locate any absolute extrema that may exist.

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Patrina SchowalterLv2

8 Dec 2018

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4. For the function 22 - 1 f(0) = 72-4 determine all of the following if they are present: (i) critical points (where f'(x) = 0 or f'(x) does not exist), local maxima and minima, intervals where f(x) is increasing or decreasing; (ii) inflection points and intervals where f(2) is concave upward or downward; (iii) asymptotes (horizontal, vertical). Sketch the graph of y = f(c), giving the (x,y) coordinates for all of the points of interest above. Please make your sketch big enough to see clearly all features of interest. 6(3.x2 + 4) You may use, without demonstrating it, the fact that f"(x) = ? (x2 – 4)3

(1 + 4)'(4.-5) and Problem 7 Let f(z) = (+4)(x-3) 50 50 _3(2 + 4)(2x + 1) 4. You must show your work in all the steps below in order to receive full credit. 25 a) (6 points) Find the x and y-coordinates of all local maxima and minima. b) 4 points Find the intervals of increase and decrease. c) [6 points) Find the r and y-coordinates of all the inflection points. d) (4 points) Find the intervals of concavity. f) 16 points) Sketch the graph of the function, clearly indicating all the intercepts, local maxima and minima, and points of inflection.

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 ?

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