Question

locate the extrema for the graph of y = f(x). name and classify the extrema of the function. 13. locate the extrema for the graph of y = f(x). name and classify the extrema of the function. 18.

Explanation:

Step1: Recall extrema definitions

Extrema are the maximum and minimum points of a function. A relative (local) maximum is a point where the function value is greater than the values at nearby points, and a relative (local) minimum is a point where the function value is less than the values at nearby points.

Step2: Analyze graph 13

Looking at the graph of \(y = f(x)\) in problem 13, we can see that there is a peak. This peak is a relative maximum. Let's assume the \(x -\)coordinate of the peak is \(x = a\). The function changes from increasing to decreasing at this point.

Step3: Analyze graph 18

For the graph of \(y = f(x)\) in problem 18, we observe a valley - like point. This is a relative minimum. Let's assume the \(x -\)coordinate of the valley is \(x = b\). The function changes from decreasing to increasing at this point.

Answer:

For problem 13: There is a relative maximum.
For problem 18: There is a relative minimum.