Chapter 4 - Section 4.3 - How Derivatives Affect the Shape of a Graph - 4.3 Exercises - Page 300: 7

(a) $x = 3$ $x = 5$ (b) $x = 2$ $x = 4$ $x = 6$ (c) $x = 1$ $x = 7$

(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: $x = 1$ $x = 7$