For each of the following functions, (1) investigate the successive derivatives and (2) evaluate them at x = 2.

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(a) f(x) = 2x +7x+9x-2 (1) f'(x)=6x + 14x+9 f"(x) = 12x + 14 f""(x) = 12 (4) (x) = 0 (b) y (6x+7)(3x-8) (1) y (6x+7)(3) + (3x-8)(6) = y' = 36x-27 y" = 36 y"" = 0 (c) f(x) = (8x)4 (1) Dx=4(8x) (-1) = -4(8-x) D= -12(8x)(1) = 12(8 - x) D =24(8x)(-1) = -24(8x) D = -24(-1) = 24 D = 0 (2) f'(2)=6(2) + 14(2) +961 f" (2) 12(2) + 14 = 38 = f"" (2) = 12 (4) (2)=0 (2) y (2) 36(2)- 27 = y' (2) = 45 y" (2) = 36 y"" (2) = 0 (2) D (2)=-4(6) = -864 D(2) = 12(6) = 432 D(2)=-24(6)=-144 D(2) = 24 D (2) = 0