(a) Find the critical values,

(b) test for concavity to determine relative maxima or minima,

(c) check for inflection points,

(d) evaluate the function at the critical values and inflection points, and (e)

graph the function, given

With f″(6) = 0 and concavity changing between x = 3 and x = 9, as seen in part (b), there is an inflection point at x = 6.

(e) See Fig. 10-15.

Transcribed Image Text:

(a) f(x) = x-18x2 +81x-58 f'(x) = 3x-36x +81 = 3(x - 12x+27) = 0 f'(x)=3(x-3)(x-9) = 0 x = 3 x=9 critical values f"(x)=6x-36 (b) f" (3)=6(3)-36 = -18 < 0 (c) concave, relative maximum f" (9)=6(9) - 36 = 18 > 0 convex, relative minimum f"=6x-36=0 x=6 possible inflection point