Question

refer to the graph of ( y = f(x) ) shown on the right. find the absolute minimum and the absolute maximum over the interval (1,18).

identify the absolute minimum. select the correct choice below fill in any answer boxes within your choice.

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

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

c. there is no absolute minimum.

Explanation:

Step1: Understand the concept of absolute minimum

The absolute minimum of a function \(y = f(x)\) over an interval \([a,b]\) is the smallest \(y -\)value (output of the function) that the function attains within that interval.

Step2: Analyze the graph

Looking at the graph of \(y = f(x)\) over the interval \([1,18]\). We observe that the function has two points where it reaches the lowest \(y -\)value. The \(y -\)value (since \(y = f(x)\)) at these points is approximately \(5\) (rounding to the nearest integer). The \(x -\)values (input of the function) corresponding to this minimum \(y -\)value are approximately \(x = 3\) and \(x = 10\) (rounding to the nearest integer).

Answer:

A. The absolute minimum is \(5\) at \(x = 3\) and \(x = 10\).