Question

use the graph of ( y = f(x) ) to answer the questions. complete parts a through j.

(tyge integers or fractions )

d. there are no relative minima

e. for what value(s) of ( x ) does ( f ) obtain a relative maximum? what are the relative maxima? select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

a. there is only one relative maxima. the maximum value is and it occurs at ( x = )

(type integers or fractions.)

b. there are two relative maxima. the leftmost maximum value is and it occurs at ( x = ). the rightmost maximum value is and it occurs at ( x = )

(type integers or fractions.)

c. there are three relative maxima. the leftmost maximum value is and it occurs at ( x = ). the central maximum value is and it occurs at ( x = ). the rightmost maximum value is and it occurs at ( x = )

(type integers or fractions.)

d. there are no relative maxima.

Explanation:

To determine the relative maxima of the function \(y = f(x)\) from its graph, we look for the points where the function changes from increasing to decreasing. A relative maximum is a point on the graph where the function has a "peak" in its local neighborhood.

Looking at the given graph:

• The left - hand side peak occurs at the point \((- 6,5)\)
• The right - hand side peak occurs at the point \((6,5)\)

So, there are two relative maxima.

Answer:

B. There are two relative maxima. The leftmost maximum value is \(5\), and it occurs at \(x=-6\). The rightmost maximum value is \(5\), and it occurs at \(x = 6\)