(a) a function value f(a) is a local maximum value of f if f(a) is the value of f on some open interval…

(a) a function value f(a) is a local maximum value of f if f(a) is the value of f on some open interval containing a. from the graph of f we see that there are two local maximum the open interval (1, 7): one local maximum is, and it occurs when x = 2; the other loca largest smallest, and it occurs when x = (b) the function value f(a) is a local minimum value of f if f(a) is the value of f on some open interval containing a. from the graph of f we see that there is one local minimum value of f on the open interval (1, 7). the local minimum value is, and it occurs when x =

(a) a function value f(a) is a local maximum value of f if f(a) is the value of f on some open interval containing a. from the graph of f we see that there are two local maximum the open interval (1, 7): one local maximum is, and it occurs when x = 2; the other loca largest smallest, and it occurs when x = (b) the function value f(a) is a local minimum value of f if f(a) is the value of f on some open interval containing a. from the graph of f we see that there is one local minimum value of f on the open interval (1, 7). the local minimum value is, and it occurs when x =

Answer

Explanation:

Step1: Recall local - maximum definition

A local maximum of a function (y = f(x)) is the largest value of (f) in some open - interval containing the point of interest.

Step2: Identify local maxima from the graph

Looking at the graph in the open interval ((1,7)), when (x = 2), we can see that (f(2)) is a local maximum. Another local maximum occurs when (x=5). We estimate the (y) - values from the graph. Let's assume the (y) - value at (x = 2) is (y_1) and at (x = 5) is (y_2). By observing the graph, if the grid lines are of unit length, (f(2)=5) and (f(5)=4).

Step3: Recall local - minimum definition

A local minimum of a function (y = f(x)) is the smallest value of (f) in some open - interval containing the point of interest.

Step4: Identify local minimum from the graph

In the open interval ((1,7)), the local minimum occurs at (x = 3), and by observing the graph, (f(3)=2).

Answer:

(a) largest; (5); (2); (4); (5) (b) smallest; (2); (3)