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

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. (1) $f$ is an odd function.

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

  3. (3) $x=1$ is a point of maxima and $x=-1$ is a point of minima of $f$.

  4. (4) $x=1$ is a point of minima and $x=-1$ is a point of maxima of $f$.

Correct Option: , 4

Solution:

$f(x)=a x^{5}+b x^{4}+c x^{3}$

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