### Home > CALC > Chapter 5 > Lesson 5.1.4 > Problem 5-43

Using the graph of the slope function below, determine where the following situations occur for

*:*

Notice that this is a graph of, but you are being asked about

*.*

Relative minima and maxima.

Relative minima and maxima can exist when

.,andBut which indicates a max and which indicates a min?To distinguish between a relative minimum and a relative maximum, use the 1st or 2nd derivative test.

Refer to the hints in problem 5-42 for more guidance.

Intervals at which

is increasing.increases when the slope is positive... and we are looking at graph of the slopes.Inflection points.

Inflection points can happen where

... and we are looking at the graph of.Intervals at which

is concave up and concave down.is concave up when... and we are looking at a graph of.