Question

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

Explanation:

Step1: Define relative maximum

A relative maximum is a point on a graph where the function changes from increasing to decreasing, so the point is higher than its immediate neighbors.

Step2: Analyze each point

• Point \(a\): It's an x - intercept, the function is increasing before and after? No, before \(a\) the function is going down, after \(a\) it's going up, so not a relative max.
• Point \(b\): Before \(b\) the function is increasing (from \(a\) to \(b\)), after \(b\) the function is decreasing (from \(b\) to \(c\) to \(d\)), so \(b\) is a relative maximum.
• Point \(c\): It's an x - intercept, the function is decreasing before and increasing after? No, before \(c\) (from \(b\) to \(c\)) it's decreasing, after \(c\) (from \(c\) to \(d\)) it's still decreasing, then increasing. So not a relative max.
• Point \(d\): It's a relative minimum (function changes from decreasing to increasing), not a max.
• Point \(e\): It's an x - intercept, function is increasing before (from \(d\) to \(e\)) and after (from \(e\) onwards), so not a relative max.

Answer:

1