the graph of a function f is given. use the graph to find each of the following.\na. the numbers, if any, at…

the graph of a function f is given. use the graph to find each of the following.\na. the numbers, if any, at which f has a relative maximum. what are these relative maxima?\nb. the numbers, if any, at which f has a relative minimum. what are these relative minima?\na. 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.\na. 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.)\nb. the function f has no relative maxima.\nb. 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.\na. the function f has (a) relative minima(minimum) at and the relative minima(minimum) are(is) . (use a comma to separate answers as needed.)\nb. the function f has no relative minima.

the graph of a function f is given. use the graph to find each of the following.\na. the numbers, if any, at which f has a relative maximum. what are these relative maxima?\nb. the numbers, if any, at which f has a relative minimum. what are these relative minima?\na. 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.\na. 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.)\nb. the function f has no relative maxima.\nb. 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.\na. the function f has (a) relative minima(minimum) at and the relative minima(minimum) are(is) . (use a comma to separate answers as needed.)\nb. the function f has no relative minima.

Answer

Explanation:

Step1: Recall relative - maximum and minimum definitions

A relative maximum of a function (y = f(x)) occurs at a point (x = c) if (f(c)\geq f(x)) for all (x) in some open interval containing (c). A relative minimum occurs at a point (x = c) if (f(c)\leq f(x)) for all (x) in some open interval containing (c).

Step2: Analyze the graph for relative maxima

By observing the graph, we can see that the function reaches a peak at (x = 1) and the (y) - value at this peak is (y = 4). So the function has a relative maximum at (x = 1) and the relative - maximum value is (4).

Step3: Analyze the graph for relative minima

Upon observing the graph, we note that there are no points where the function has a local trough (a point lower than the surrounding points in an open interval). So the function has no relative minima.

Answer:

a. A. The function f has (a) relative maxima(maximum) at 1 and the relative maxima(maximum) are(is) 4. b. B. The function f has no relative minima.