### Home > CALC3RD > Chapter Ch5 > Lesson 5.1.4 > Problem 5-43

Using the graph of the slope function at right, determine where the following situations occur for :

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

*.*

Relative minima.

Relative minima and maxima can exist when

.

This occurs when, and. But which points indicate a maximum and which indicate a minimum?A minimum occurs when the slope changes from negative to positive.

Relative maxima.

See the hint in part (a). A maximum occurs when the slope changes from positive to negative.

Interval(s) over which

is increasing.is increasing when.

Inflection points

*.*Inflection points can happen where

. Remember, we are looking at the graph of.

Interval(s) over which

is concave up.is concave up when.

Interval(s) over which

is concave down.is concave down whenis decreasing.