Given said graph, find: a. The open intervals on which f is increasing b. The op

Question

Given said graph, find:

a. The open intervals on which f is increasing

b. The open intervals on which f is decreasing

c. The open intervals on which f is concave upward

d. The open intervals on which f is concave downward

e. Inflection points

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Given said graph, find: The open intervals on which f is increasing The open intervals on which f is decreasing The open intervals on which f is concave upward The open intervals on which f is concave downward Inflection points

Explanation / Answer

Assuming the graph is for f(x)

increasing/decreasing intervals refer to + and - slope, respectively

critical values (where f ' (x) or m = 0 or is undefined): x = -8, -2, 1, 3, 5

a) increasing/positive slope on: (-8, -2) U (1, 3) U (5, 10)

b) decreasing/negative slope on: (-10, -8) U (-2, 1) U (3, 5)

concavity refers to the parabolic shapes of the curve

upward parabola = concave up

downward parabola = concave down

inflection point = change in concavity

c) concave up: (-10, -5)

d) concave down: (-5, 1) U (1, 5)

e) inflection points: x = -5

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