Using the graph of the slope function at right, determine where the following situations occur for g : Homework Help ✎
Interval(s) over which g is increasing.
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.