Question

1. consider the adjacent graph:

7a does the function have an absolute maximum or minimum?
the correct option was a
yes, it has an absolute maximum. a
no, it does not have either. b
yes, it has an absolute minimum. c
5 well done!
7b are there any local maximums or minimums? select all that apply.
no, there are neither. a yes, there are local minimums. b yes, there are local maximums. c

Explanation:

Step1: Analyze local minima

A local minimum is a point where the function changes from decreasing to increasing. Looking at the graph, at \(x = 2\), the function has a local minimum.

Step2: Analyze local maxima

A local maximum is a point where the function changes from increasing to decreasing. Looking at the graph, there is a point between \(x=2\) and \(x = 3\) where the function has a local maximum.

Answer:

B. Yes, there are local minimums.
C. Yes, there are local maximums.