(b) Find and classify all critical points of f. (Classify means determine if they are local max/min or neither.) No f'DNE crit pts to crit pts are x=0,3 By 1st Devil. Test& : X= neither *=3 loc.max The local minima are at x = The local maxima are at x =_- are neither local maxima, nor local The critical point(s) r=__ minima.

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Reid WolffLv2

6 Oct 2018

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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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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

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