Question

In the polynomial shown in the graph below, are there any places that could be described as either a local minimum or local maximum? Neither? Both?

Answer 1

Local Min and Local Max

Explanation:

Since our end behavior of our graph is goes on to infinity and negative infinity, we know that we will not have an absolute min or max. However, we will have relative/local min and max.

The local min and max are mins and maxes relative to the surrounding points. We see that our local min would happen around x ≈ 0.75 and our local max will happen at x ≈ -1.9.