Redo Problem 10.11, given f(x) = 2x3 12x2 72x 70. (a) (b) f'(x)=-6x + 24x +

Redo Problem 10.11, given f(x) = –2x3 12x2 72x – 70.

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(a) (b) f'(x)=-6x + 24x + 72=-6(x - 4x - 12) = 0 f'(x)=-6(x+2)(x-6)=0 x = -2 x=6 f"(x)=-12x+24 critical values f"(-2)=-12(-2) + 24 = 48 > 0 convex, relative minimum f" (6)=-12(6) + 24 = -48 < 0 concave, relative maximum (c) f"(x)=-12x + 24 = 0 x = 2 inflection point at x = 2 (d) f(-2)=-150 (-2,-150) relative minimum f(2) = 106 (2, 106) inflection point f(6) = 362 (6, 362) relative maximum (e) See Fig. 10-16.