−), and also as x increases through 2 (− to +). Thus both (0, 0) and (2, −16)
are inflection points of the curve.The curve is sketched in Figure N4–5.
Figure N4–5Verify the preceding on your calculator.
Case II. Functions Whose Derivatives May Not Exist Everywhere
If there are values of x for which a first or second derivative does not exist, we
consider those values separately, recalling that a local maximum or minimum
point is one of transition between intervals of rise and fall and that an inflection
point is one of transition between intervals of upward and downward concavity.
Example 14 __
Sketch the graph of y = x2/3.
SOLUTION:.