Question

Use the graph of f below to classify the following extreme values. I hope the picture is clear and help, please?

Answer 1

Please see below.

Explanation:

The relative minimum value of `f` are `(-2,-1)` and `(2,-4)`.

The relative maximum value of `f` are `(1,3)` and `(6,8)`.

As the function appears to be continuously declining even below relative minimum values, hence there is no absolute minimum.

The pattern of function for `x<-5` is not apparent, but function appears to be flat at `x=-5`, the possibility of absolute maxima is at `(6,8)`.

The critical numbers are where value of first derivative is `0` i.e. curve is flat. This appears at `x=-2`, `x=1`, `x=2` and `x=6`.