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

Jan 7, 2016

$f \left(x\right) = \frac{1}{3} {x}^{3} - \frac{3}{2} {x}^{2} + \frac{13}{3}$

#### Explanation:

Integrating f(x): ${x}^{3} / 3 - \frac{3}{2} {x}^{2} + c$

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

$\Rightarrow {2}^{3} / 3 - 3 \times {2}^{2} / 2 + c = 1$

$\Rightarrow \frac{8}{3} - 6 + c = 1$

$\Rightarrow c = 1 + 6 - \frac{8}{3} = \frac{13}{3}$

$\Rightarrow f \left(x\right) = \frac{1}{3} {x}^{3} - \frac{3}{2} {x}^{2} + \frac{13}{3}$