Question

refer to the graph of ( y = f(x) ) shown on the right. find the absolute minimum and the absolute maximum over the interval (1,15).
identify the absolute maximum. select the correct choice below fill in any answer boxes within 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: Understand the concept of absolute maximum

The absolute maximum of a function \(y = f(x)\) on an interval \([a,b]\) is the largest value of \(y\) (i.e., \(f(x)\)) for \(x\in[a,b]\).

Step2: Analyze the graph

Looking at the graph of \(y = f(x)\) on the interval \([1,15]\), we can see that as \(x\) approaches \(15\), the function value is increasing. The highest point on the graph within the interval \([1,15]\) occurs at \(x = 15\).

Answer:

B. The absolute maximum is \(16\) at \(x = 15\)