Single Variable Calculus, Chapter 4, 4.3, Section 4.3, Problem 2

Below is the graph of $f$




a.) Find the open intervals on which $f$ is increasing.
b.) Find the open intervals on which $f$ is decreasing.
c.) Find the open intervals on which $f$ is concave upward.
d.) Find the open intervals on which $f$ is concave downward.
e.) Find the coordinates of the points of inflection.

a.) Based from the graph, the function is increasing at intervals $ 0 < x < 1 $ and $ 3 < x < 7$
b.) Based from the graph, the function is decreasing at interval $1 < x < 3$
c.) Based from the graph, the function has upward concavity at interval $2 < x < 4$ and $5 < x < 7$
d.) Based from the graph, the function has downward concavity at interval $0 < x < 2$ and $ 4 < x < 5$
e.) The points of inflections are at $(2,2), (4,3)$ and $(5,4)$

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