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: Identify the lowest point on the graph in the interval [0,10]

By observing the graph, we can see that there is a single lowest - point (local minimum which is also the absolute minimum in the given interval).

Step2: Determine the \(y\) - value (function value) and \(x\) - value of the absolute minimum

Looking at the grid - like structure of the graph (assuming each square is of unit length), the \(y\) - value (function value) of the absolute minimum is \(5\) and the \(x\) - value is \(8\).

Answer:

B. The absolute minimum is \(5\) at \(x = 8\)