For each of the following functions, (1) find the second-order derivative and (2) evaluate it at x = 3.

Practice the use of the different second-order notations.

Transcribed Image Text:

(a) y 10x3 +8x + 19 (1) dy dx d y dx = 30.x2 +16.x = 60x+16 (b) f(x)=3x+5x +6x (1) f'(x)=12x3 + 15x +6 f" (x)=36x+30x (c) f(x)=(4x-1) (3x+2) (1) f'(4x-1) (6x) + (3x + 2)(4) f' = 24x-6x + 12x +8 f' = 36.x-6x+8 f" = 72x-6 (2) At x = 3, d y dx2 = 60(3) +16 196 (2) At x = 3, = f" (3)=36(3)+30(3) = 414 (2) At x = 3, f" (3) = 72(3) - 6 f" (3) = 210