Let `f(x) = x^50-x^20` STATEMENT-1: Global maximum of f(x) in `[0, 1]` is 0 STATEMENT-2 : x = 0 is a stationary point of f(x)

Let f(x) be a polynomial of degree three f(0) = -1 and f(1) = 0. Also, 0 is a stationary point of f(x). If f(x) does not have an extremum at x=0, then the value of integral int(f(x))/(x^3-1)dx, is

Let f(x) be a polynomial of degree three f(0)=-1 and f(1)=0. Also,0 is a stationary point of f(x). If f(x) does not have an extremum at x=0, then the value of integral int(f(x))/(x^(3)-1)dx, is

Let f(x) =(x+1)^(2) - 1, x ge -1 Statement 1: The set {x : f(x) =f^(-1)(x)}= {0,-1} Statement-2: f is a bijection.

Statement-1 : Let f(x) = |x^2-1|, x in [-2, 2] => f(-2) = f(2) and hence there must be at least one c in (-2,2) so that f'(c) = 0 , Statement 2: f'(0) = 0 , where f(x) is the function of S_1

Let f(x) = {(|x|, for 0 <|x| < 2)= 1,for x =0 } Then at x = 0, f (x) has

Let g(x) = f(f(x)) where f(x) = { 1 + x ; 0 <=x<=2} and f(x) = {3 - x; 2 < x <= 3} then the number of points of discontinuity of g(x) in [0,3] is :

Deine F(x) as the product of two real functions f_1(x) = x, x in R, and f_2(x) ={ sin (1/x), if x !=0, 0 if x=0 follows : F(x) = { f_1(x).f_2(x) if x !=0, 0, if x = 0. Statement-1 : F(x) is continuous on R. Statement-2 : f_1(x) and f_2(x) are continuous on R.