Let f(x) be a polynomial of degree 5 such

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Question:

Let $f(x)$ be a polynomial of degree 5 such that $x=\pm 1$ are its critical points. If

$\lim _{x \rightarrow 0}\left(2+\frac{f(x)}{x^{3}}\right)=4$, then which one of the following is not true?

 

  1. $f$ is an odd function

  2. $x=1$ is a point of minima and $x=-1$ is a point of maxima of $f$.

  3. $x=1$ is a point of maxima and $x=-1$ is a point of minimum of $f$.

  4. $f(1)-4 f(-1)=4$

Correct Option: , 2

Solution:

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