Question

Let f(x) be a polynomial of degree 5 such that x = ±1 are its critical points. If lim(x→0) (2 + f(x)/x³) = 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) – 4f(–1) = 4

Answer 1

Answer is (2)

Minima at x = -1

Maxima at x = 1

Answer 2

Answer is (1)

f(x) = ax⁵ + bx⁴ + cx³