Answer
See below.
Work Step by Step
In the graph of a function $f(x)$, a point of inflection $[c, f(c)]$ occurs where the concavity changes.
Significance:
a. When $f'' (x) \gt 0$ on an interval $[a,b]$, then $f(x)$ is concave up on that interval.
b. When $f'' (x) \lt 0$ on an interval$[a,b]$, then $f(x)$ is concave down on that interval.
c. When $f'' (x)$ changes sign from positive to negative, or from negative to positive at a point $x = c$, then there is an inflection point located at $x = c$ on the curve.
