Question

What is `f(x) = int x^2 - 3x` if `f(2)=1`?

Answer 1

`f(x) = 1/3x^3 - 3/2x^2 + 13/3`

Explanation:

Integrating f(x): `x^3/3 - 3/2x^2 + c`

f(2 ) = 1 enables the constant of integration ( c ) to be found by evaluating for x = 2 , y = 1

`rArr 2^3/3 -3 xx 2^2/2 + c = 1`

`rArr 8/3 - 6 + c = 1`

`rArr c = 1 + 6 - 8/3 = 13/3`

`rArr f(x) = 1/3 x^3 - 3/2 x^2 + 13/3`