The graph of the derivative f of a continuous function f is shown. On what inter

Question

The graph of the derivative f of a continuous function f is shown. On what interval(s) is f increasing? (Enter your answer using interval notation.) On what interval(s) is f decreasing? (Enter your answer using interval notation.) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.) At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) On what interval(s) is f concave upward? (Enter your answer using interval notation.) On what interval(s) is f concave downward? (Enter your answer using interval notation.) State the x-coordinate(s) of the point(s) of inflection. (Enter your answers as a comma-separated list.) Assuming that f (0) = 0, sketch a graph of f. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

a) increasing (1, 6) and (8, inf)

decreasing (-2, 1) and (6, 8)

b) maxima x=6 minima x=1, 8

c) concave up (-2, 2) (3,5)and (7, inf)

concave down (2,4) and (5,7)

d)points of inflection 2, 5, 7

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