Answer
a) Increasing on $(0,2)\cup(4,6)\cup(8,\infty)$ and decreasing on $(2,4)\cup(6,8)$
b) Local maxima: $x$ = $2$ and $x$ = $6$; local minima: $x$ = $4$ and $x$ = $8$
c) Concave upward: $(3,6)\cup(6,\infty)$; concave downward: $(0,3)$
d) Point of inflection: $x = 3$
e) See graph
Work Step by Step
a) $f$ is increasing where $f'$ is positive, that is on $(0,2)$, $(4,6)$ and $(8,\infty)$ and decreasing where $f'$ is negative, that is on $(2,4)$ and $(6,8)$
b) $f$ has local maxima where $f'$ changes from positive to negative at $x$ = $2$ and at $x$ = $6$ and local minima where $f'$ changes from negative to positive at $x$ = $4$ and $x$ = $8$
c) $f$ is concave upward where $f'$ is increasing, that is on $(3,6)$ and $(6,\infty)$ and concave downward where $f'$ is decreasing that is on $(0,3)$
d) There is a point of inflection where $f$ changes from being concave downward to being concave upward, that is at $x = 3$
e) As picture below
