## Calculus: Early Transcendentals 8th Edition

(a) The intervals when $f$ is increasing: $(0,4)$ $(6,8)$ (b) The values when $f$ has a local maximum: $x = 4$ $x = 8$ The value when $f$ has a local minimum: $x = 6$ (c) The intervals when $f$ is concave upward: $(0,1)$ $(2,3)$ $(5,7)$ The intervals when $f$ is concave downward: $(1,2)$ $(3,5)$ $(7,9)$ (d) The inflection points are: $x = 1$ $x = 2$ $x = 3$ $x = 5$ $x = 7$
(a) $f$ is increasing when $f' \gt 0$ The intervals when $f$ is increasing: $(0,4)$ $(6,8)$ (b) $f$ has a local maximum when $f'$ changes from positive to negative. $f$ has a local minimum when $f'$ changes from negative to positive. The values when $f$ has a local maximum: $x = 4$ $x = 8$ The value when $f$ has a local minimum: $x = 6$ (c) $f$ is concave upward when $f'$ is increasing. $f$ is concave downward when $f'$ is decreasing. The intervals when $f$ is concave upward: $(0,1)$ $(2,3)$ $(5,7)$ The intervals when $f$ is concave downward: $(1,2)$ $(3,5)$ $(7,9)$ (d) The inflection points are the points where the $f'(x) = 0$ at a local maximum or a local minimum. The inflection points are: $x = 1$ $x = 2$ $x = 3$ $x = 5$ $x = 7$