Question

the function $f(x)$ is graphed below. how many points on the graph represent a relative maximum?

Explanation:

Step1: Recall the definition of relative maximum

A relative maximum of a function \(y = f(x)\) is a point \((x_0,y_0)\) on the graph of the function such that \(y_0\geq f(x)\) for all \(x\) in some open interval containing \(x_0\). Geometrically, at a relative maximum, the function changes from increasing to decreasing.

Step2: Analyze the graph

Looking at the graph of \(y = f(x)\), we check the behavior of the function at each critical - like point.

• At point \(d\): The function changes from increasing (to the left of \(d\)) to decreasing (to the right of \(d\)).
• At point \(h\): The function changes from increasing (to the left of \(h\)) to decreasing (to the right of \(h\)).

Answer:

\(2\)