Question

Given f"(x) = 2, f'(1)=4, and f(2)=-2,
find f(x).

Answer 1

Explanation:

f"(x)=2

integrating

f'(x)=2x+c

f'(1)=2+c=4

c=4-2=2

f'(x)=2x+2

integrating

f(x)=2x^2/2+2x+a

f(x)=x^2+2x+a

f(2)=-2

(2)^2+2(2)+a=-2

4+4+a=-2

a=-2-8=-10

f(x)=x^2+2x-10