Redo Problem 10.6, given y = (6 – x)3.

Continuing to take successively higher-order derivatives and evaluating them at the critical value in search of the first higher-order derivative that does not equal zero,

As explained in Section 10.7, with the first nonzero higher-order derivative an odd-numbered derivative, y is at an inflection point and not at an extreme point. See Fig. 10-11.

Transcribed Image Text:

(1) (2) y' = 3(6x)2(-1)=-3(6x) = 0 == x=6 critical value y"=-6(6x)(-1) = 6(6-x) y" (6)=6(66) = 0 test inconclusive