Question

the graph of a function f is given. use the graph to find each of the following. a. find the numbers, if any, at which f has a relative maximum, and find the relative maxima(maximum). select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. the function f has (a) relative maxima(maximum) at 1 and the relative maxima(maximum) are(is) 4. (use a comma to separate answers as needed.) b. the function f has no relative maxima. b. find the numbers, if any, at which f has a relative minimum, and find the relative minima(minimum). select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. the function f has (a) relative minima(minimum) at and the relative minima(minimum) are(is). (use a comma to separate answers as needed.) b. the function f has no relative minima.

Explanation:

Step1: Recall relative - maximum and minimum definition

A relative maximum of a function occurs at a point where the function changes from increasing to decreasing. A relative minimum occurs at a point where the function changes from decreasing to increasing.

Step2: Analyze the graph for relative maxima

By looking at the graph (not shown here but based on the given answer for part a), we can see that at \(x = 1\), the function changes from increasing to decreasing and the \(y\) - value at \(x = 1\) is \(y=4\).

Step3: Analyze the graph for relative minima

We need to look for points on the graph where the function changes from decreasing to increasing. If there are such points, we record the \(x\) - values (where the change occurs) and the corresponding \(y\) - values. If there are no such points, we choose option B.

Answer:

a. A. The function f has (a) relative maxima(maximum) at 1 and the relative maxima(maximum) are(is) 4.
b. (Since no graph is provided, assume we need to analyze it) If there are points where the function changes from decreasing to increasing, fill in the \(x\) - values and \(y\) - values in option A. If not, B. The function f has no relative minima.