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> Let $P(x)$ be a polynomial of degree 4 , having extremum at $x=1,x=2$ and $$\lim\_{x\to 0}\frac{x^2+P(x)}{x^2}=2.$$ Then what is the value of $P(2)$?
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I worked out the limit using L'Hospital got a relation in terms of second derivative of $P$; the other derivative relations are that first derivatives are zero at 1,2. 

How can we interpretate these derivative equations to find the function?

Any help is welcome.