find f if f''(x)=4-6x

Question

Find f if f′′(x)=4−6x, f(0)=3, and f(2)=−8.

 

f(x)=_____

Answer 1

F"(x) = 4 -6x

F'(x) = 4x -3x² +K₁

F(x) = 2x² -x³ +K₁x + K₂

F(0) = 3 implies K₂ = 3

F(2) = -8 implies K₁ = -11/2

So, F(x) = 2x² -x³ -(11/2)x + 3