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
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 when is decreasing.