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**DarkestEvil** Let $\displaystyle f$ be a differentiable function, defined for all real numbers $\displaystyle x$, with the following properties. Find $\displaystyle f(x)$. Show your work.

- $\displaystyle f '(x)=ax^2 + bx$

- $\displaystyle f '(1)=6$ and $\displaystyle f ''(1)=18$

. $\displaystyle 2$

- ∫$\displaystyle f(x)dx=18$

. $\displaystyle 1$

I am completely lost on this question. I assume that I have to take the anti derivative of the first given property by using the second given to solve for the values of a and b, but I'm not sure how to do it.