Absolute extrema on an interval

[john3j]

Hello,

I have a question on my homework that I do not understand. We are supposed to find the absolute extrema for the graph of f(x) on the given interval. Here is the problem:
.
I know how to find the absolute extrema with a function, but not based off of a graph because the function is not given. I think that the absolute maximum would be (-3, 5) and the absolute minimum would be (3, 4), but I am not sure if that is right or not. Could anyone clarify for me?

Thanks,
John

 

[JeffM]

Hello,

I have a question on my homework that I do not understand. We are supposed to find the absolute extrema for the graph of f(x) on the given interval. Here is the problem:
View attachment 2489.
I know how to find the absolute extrema with a function, but not based off of a graph because the function is not given. I think that the absolute maximum would be (-3, 5) and the absolute minimum would be (3, 4), but I am not sure if that is right or not. Could anyone clarify for me?

Thanks,
John

The absolute maximum on that interval is indeed 5 because that is the highest point that the graph hits over the interval [-4, 5]. And you are correct that the absolute maximum occurs at x = - 3.

But the absolute minimum, the lowest point that the graph hits over the interval [-4, 5], is - 2, which occurs when x = 5.

Absolute extrema over an interval are the highest and lowest values that the function achieves (the highest and lowest points that the graph hits). An absolute extremum over an interval is either a local extremum for some sub-interval or an end-point.