Given
f ''(x)=6x–4 and f '(0)=1 and f(0)=5
find f '(x) and f (1)
just work backwards, one level at a time:
f ''(x) = 6x-4
f'(x) = 3x^2 - 4x + a
f(x) = x^3 - 2x^2 + ax + b
f'(0) = 3*0 - 4*0 + a = 1, so a=1
f(0) = b, so b=5
and
f(x) = x^3 - 2x^2 + x + 5