## Precalculus (6th Edition) Blitzer

Consider the fact that the graph decreases in an interval $\left( -\infty ,a \right)$ and increases in an interval $\left( a,\infty \right)$. This means that the point $a$ is a critical point as after that point the nature of the graph is changed from decreasing to increasing. This implies $f\left( a \right)$ is not a relative maximum. If the graph is decreasing on $\left( -\infty ,a \right)$ and increasing on $\left( a,\infty \right)$ , then $f\left( a \right)$ must be a relative minimum. Hence, this statement does not make any sense and $f\left( a \right)$ is a relative minimum.