Question

question 2 · 1 point consider the graph of f(x) below. how many local maxima does f(x) have? select the correct answer below: 0, 1, 2, 3, 4

Explanation:

Step1: Recall local maxima condition

A function \( f(x) \) has a local maximum where \( f'(x) \) changes from positive to negative (by the First Derivative Test).

Step2: Analyze \( f'(x) \) graph

We look for points where the graph of \( f'(x) \) crosses from above the \( x \)-axis (positive) to below the \( x \)-axis (negative). From the given graph of \( f'(x) \), we observe how many times this sign change (positive to negative) occurs. By examining the graph, we see that there is 1 such point where \( f'(x) \) goes from positive to negative.

Answer:

1