Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points. If $\mathop {\lim }\limits_{x \to 0} \left( {2 + {{f\left( x \right)} \over {{x^3}}}} \right) = 4$, then which one of the following is not true?

Question

Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points.

If $\mathop {\lim }\limits_{x \to 0} \left( {2 + {{f\left( x \right)} \over {{x^3}}}} \right) = 4$, then which one of the following is not true?

ƒ(1) - 4ƒ(-1) = 4.

x = 1 is a point of minima and x = -1 is a point of maxima of ƒ.

x = 1 is a point of maxima and x = -1 is a point of minimum of ƒ.

ƒ is an odd function.

Solution

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