Find f.

Question

f ''(x) = −2 + 12x − 12x2, f(0) = 9, f '(0) = 14

Answer 1

d^2y/dx^2 = -12 x^2 + 12 x - 2
dy/dx = - 4 x^ 3 + 6 x^2 - 2 x + c
at = 0 dy/dx = 14 so c = 14
dy/dx = - 4 x^ 3 + 6 x^2 - 2 x + 14
y = - x^4 + 2 x^3 - x^2 + 14 x + d
at 0 , y = d = 9
so
y = - x^4 + 2 x^3 - x^2 + 14 x + 9

Answer 2

almost the same as
https://www.jiskha.com/display.cgi?id=1525996280

keep integration to go from f''(x) to f'(x) to f(x)
make sure you find the value of the constant in each step