Question

for the graph of ( y = f(x) ) shown to the right, find the absolute minimum and the absolute maximum over the interval (0,10).
select the correct choice below and, if necessary, fill in the answer boxes to complete 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: Analyze the graph

The absolute minimum of a function on a closed interval \([a,b]\) is the lowest \(y -\) value of the function on that interval.

Step2: Locate the lowest \(y -\) value

Looking at the graph of \(y = f(x)\) on the interval \([0,10]\), we can see that the lowest \(y -\) value occurs at a single \(x -\) value.

Answer:

B. The absolute minimum is \(5\) at \(x = 6\)