## Calculus: Early Transcendentals 8th Edition

Curve a is the graph of $f$, curve b is the graph of $f''$, curve c is the graph of $f'$.
First look at curve b. Curve b has 3 local extremas (the point where the curve changes from going up to down and vice versa) and 2 times passes the $Ox$ line. Imagine if curve b represents $f$ or $f'$, there must be another curve that passes the $Ox$ 3 times to match the 3 local extremas of curve b. However, none of the remaining curves passes the $Ox$ 3 times. Therefore, curve b is the graph of $f''$. Now look at the remaining 2 curves. Curve c has 2 local extremas and 1 time passes the $Ox$ line. If curve c represents $f$, then curve a must pass the $Ox$ line 2 times to match the 2 local extremas of curve c. However, curve a does not pass the $Ox$ line at all. Therefore, curve c is the graph of $f'$ and curve a is the graph of $f$.