Use the given graph of the derivative f\' of a continuous function f over the in

Question

Use the given graph of the derivative f' of a continuous function f over the interval (0, 9) to find the following. (a) 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.) (b) At what value(s) of x does have a local maximum? (Enter your answers as a comma-separated list.) x = At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) x = (c) 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.) (d) What are the x-coordinate(s) of the inflection point(s) of f? (Enter your answers as a comma-separated list.) x =

Explanation / Answer

a)
f is increasing on (1,6)U(8,9)
f is decreasing on (0,1)U(6,8)

b)
local maxima at
x = 6

local minima at
x= 1,8

c)
concave up when slope of f'(x) is positive
concave up on (0,2)U(3,5)U(7,10)
concave down on (2,3)U(5,7)

d)
inflexion point at
x = 2,3,5,7

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