Redo Problem 10.11, given f(x) = (2x – 8)1

Continuing on to successively higher-order derivatives,

(c) As explained in Section 10.7, with the first nonzero higher-order derivative an odd-numbered derivative, the function is at an inflection point at x = 4. With an inflection point at the only critical value, there is no relative maximum or minimum.

Testing for concavity to the left (x = 3) and right (x = 5) of the inflection point,

(e) See Fig. 10-18.

Transcribed Image Text:

(a) (b) f'(x)=3(2x-8)(2) = 6(2x8) = 0 x=4 critical value f"(x) = 12(2x8)(2) = 24(2x-8) f" (4)=24(8-8)=0 test inconclusive