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

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

*g*: Homework Help ✎

Relative minima.

Relative maxima.

Interval(s) over which

*g*is increasing.Inflection points

*.*Interval(s) over which

*g*is concave up.Interval(s) over which

*g*is concave down.

Notice that this is a graph of *g*′(*x*), but you are being asked about *y* = *g*(*x*).

Relative minima and maxima can exist when *g*′(*x*) = 0.

This occurs when *x* = *a*, *x* = *d*, and *x* = *f*. But which points indicate a maximum and which indicate a minimum?

A minimum occurs when the slope changes from negative to positive.

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

*g* is increasing when *g*′(*x*) > 0.

Inflection points can happen where *g*″(*x*) = 0. Remember, we are looking at the graph of *y* = *g*′(*x*).

*g* is concave up when *g*″(*x*) > 0.

*g* is concave down when *g*′(*x*) is decreasing.