Question

If f'(x) =(2-x)^2 and the y-intercept of f(x) is 4/3, find the rule for f(x)

Answer 1

Do we have to integrate f'(x)?

Answer 2

yes

Answer 3

So from the outside it will be (....)3/3

Answer 4

\[f \left( x \right)=\int\limits \left( 2-x \right)^2 ~dx=\frac{ \left( 2-x \right)^3 }{ 3 }(-1)+c\]
when x=0,f(x)=4/3
find c