Question

choose the correct graph of the function. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (type an ordered - pair. type integers or decimals rounded to two decimal places as needed.) a. the local maximum is the local minimum is b. the local maximum is there is no local minimum c. the local minimum is there is no local maximum

Explanation:

Step1: Recall local - extrema definition

Local maximum is a point where the function changes from increasing to decreasing, and local minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze the graph

By observing the graph of the function, we look for the peaks (local maxima) and valleys (local minima). If the graph has a peak, there is a local maximum at that point's \(x - y\) coordinates, and if it has a valley, there is a local minimum at that point's \(x - y\) coordinates. If the graph has no such peaks or valleys, we say there are no local maxima or minima.

Answer:

Since the question is incomplete as the actual graph details for determining local maxima and minima are not fully clear from the provided image, we cannot give a definite answer about local maxima and minima values. But in general, if we could observe the graph properly:
If there is a point where the function changes from increasing to decreasing, the local maximum is the \(y\) - value of that point. If there is a point where the function changes from decreasing to increasing, the local minimum is the \(y\) - value of that point. If there are no such change - of - direction points, then there is no local maximum or no local minimum respectively.