HELP ME PLEASE! FIND F

Question

Find f.

f ″(x) = −2 + 36x − 12x²,    f(0) = 8,    f ′(0) = 18

f(x) =

I got -x^4+8x^3-x^2+18x+2 where did I mess up?

Answer 1

f'(x) = -4x³ + 18x² - 2x + C f'(0) = C = 18 f'(x) = -4x³ + 18x² - 2x + 18

f(x) = - x⁴ + 6x³ - x² + 18x + D. f(0) = D = 8.

f(x) = - x⁴ + 6x³ - x² + 18x + 8

Looks like you got the coefficient of the cubic term wrong in f (maybe you did 18 / 3 = 8?). Also the constant term in f clearly needs to be 8 (not 2) so that f(0) = 8.

But it looks like you are integrating (antidifferentiating) mostly very well.