Question

for the graph of ( y = f(x) ) shown to the right, find the absolute minimum and the absolute maximum over the interval (1,10).
identify the absolute minimum. select the correct choice below fill in any answer boxes within your choice.
a. the absolute minimum is at ( x = ) and ( x = )
(round to the nearest integer as needed. use ascending order.)
b. the absolute minimum is at ( x = )
(round to the nearest integer as needed.)
c. there is no absolute minimum.

Explanation:

Step1: Analyze the graph

Look at the values of \(y = f(x)\) for \(x\in[1,10]\). The absolute minimum is the lowest \(y -\)value in this interval.

Step2: Locate the minimum

By observing the graph (assuming standard grid - like graph interpretation), the lowest \(y -\)value in the interval \([1,10]\) occurs at a single \(x\) value.

Answer:

B. The absolute minimum is \(2\) at \(x = 7\) (assuming the graph shows \(y = 2\) when \(x = 7\) after proper visual inspection of the grid - based graph)