Suppose that `f` is a polynomial of degree `3` and that `f^(x)!=0` at any of the stationary point. Then `f` 1)has exactly one stationary point `f` 2)must have no stationary point `f` 3)must have exactly two stationary points `f` has 4)either zero or two stationary points.

Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.

f(x) is polynomial of degree 4 with real coefficients such that f(x)=0 satisfied by x=1, 2, 3 only then f'(1) f'(2) f'(3) is equal to -

Find the critical number and stationary point f(x) = 2x - 3x^(2)

consider the function f(X) =x+cosx -a values of a for which f(X) =0 has exactly one negative root are

consider the function f(X) =x+cosx -a values of a which f(X) =0 has exactly one positive root are

Find the critical points(s) and stationary points (s) of the function f(x)=(x-2)^(2//3)(2x+1)

If f(x) is a non-zero polynomial of degree four, having local extreme points at x=-1,0,1 then the set S={x in R:f(x)=f(0)} contains exactly (a) four rational numbers (b) two irrational and two rational numbers (c) four irrational numbers (d) two irrational and one rational number

Consider the graph of the function f(x) = x+ sqrt|x| Statement-1: The graph of y=f(x) has only one critical point Statement-2: fprime (x) vanishes only at one point

Let f(x) be a polynomial with integral coefficients. If f(1) and f(2) both are odd integers, prove that f(x) = 0 can' t have any integral root.