Answer
(a) $x = 3$
$x = 5$
(b) $x = 2$
$x = 4$
$x = 6$
(c) $x = 1$
$x = 7$
Work Step by Step
(a) If this is the graph of $f$, the inflection points are the points where the graph changes from concave up to concave down or vice versa.
The inflection points are:
$x = 3$
$x = 5$
(b) If this is the graph of $f'$, the inflection points are the points where the slope is zero at a local maximum or a local minimum.
The inflection points are:
$x = 2$
$x = 4$
$x = 6$
(c) If this is the graph of $f''$, the inflection points are the points where the graph crosses the x-axis and changes sign. These are the points where $f''(x) = 0$
The inflection points are:
$x = 1$
$x = 7$