Question

for the graph of ( y = f(x) ) shown to the right, find the absolute minimum and the absolute maximum over the interval (5, 10).

select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

○ a. the absolute maximum is (square) at ( x=square ) and ( x=square ).
(round to the nearest integer as needed. use ascending order.)

○ b. the absolute maximum is (square) at ( x=square ).
(round to the nearest integer as needed.)

○ c. there is no absolute maximum.

Explanation:

Step1: Analyze the graph on the interval [5,10]

We look at the function values \(y = f(x)\) for \(x\) from \(5\) to \(10\). The absolute maximum of a function on a closed interval \([a,b]\) is the largest \(y -\)value of the function on that interval.

Step2: Identify the endpoints and local maxima

The left - hand endpoint of the interval \([5,10]\) is \(x = 5\) and the right - hand endpoint is \(x=10\). By observing the graph (assuming standard grid where each square is of unit length), at \(x = 10\), the function value \(y=f(10)\) is larger than the function values at other points in the interval \([5,10]\).

Answer:

B. The absolute maximum is \(10\) at \(x = 10\)