Question

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

Explanation:

Step1: Recall relative maximum definition

A relative maximum is a point where the function changes from increasing to decreasing, and its \( y \)-value is greater than the \( y \)-values of neighboring points.

Step2: Analyze each point

• Point \( a \): It's an \( x \)-intercept, not a peak (function is decreasing before and increasing after? No, before \( a \) function is going up? Wait, no, looking at the graph: left of \( b \), function comes from top, goes down to \( b \), then up to \( c \), then down to \( e \), then up. Wait, point \( c \): before \( c \), function is increasing (from \( b \) to \( c \)), after \( c \), function is decreasing (from \( c \) to \( e \)? Wait, no, from \( c \) to \( d \) to \( e \), so after \( c \), function decreases. So \( c \) is a relative maximum. Points \( b \) and \( e \) are relative minima (function changes from decreasing to increasing there). Points \( a \), \( d \), \( f \) are \( x \)-intercepts, not maxima. So only 1 point (\( c \)) is a relative maximum.

Answer:

1