The function `f(x) = 1 - (x^2)^(1/3)` has zeros at `x = -1` and `x = 1`. However, `f'(x) != 0 AA x in (-1, 1)`. Explain what seems to be contradiction with Rolle's Theorem .

The function f(x)=1-(x^(2))^((1)/(3)) has zeros at x=-1 and x=1. However,f'(x)!=0AA x in(-1,1). Explain what seems to be contradiction with Rolle's Theorem.

Let f(x)=4x^(3)+x^(2)-4x-1 . The equation f(x)=0 has roots 1 and (-(1)/(4)) . Find the root of f'(x)=0 mentioned in Rolle's theorem.

Value of 'c' of Rolle's theorem for f(x) = |x| in [-1,1] is

Verify Rolles theorem for function f(x)=(x^2-1)(x-2) on [-1,\ 2]

If the function f(x) is defined by f(x)=(x(x+1))/(e^(x)) in [-1, 1], then the values of c in Rolle's theorem is -

Verify Rolles theorem for function f(x)=x(x-1)^(2) on [0,1]

Verify Rolles theorem for function f(x)=(x-1)(x-2)^(2) on [1,2]

The differentiable function y= f(x) has a property that the chord joining any two points A (x _(1), f (x_(1)) and B (x_(2), f (x _(2))) always intersects y-axis at (0,2 x _(1)x _(2)). Given that f (1) =-1. then: In which of the following intervals, the Rolle's theorem is applicable to the function F (x) =f (x) + x ? (a) [-1,0] (b) [0,1] (c) [-1,1] (d) [0,2]

Verify Rolles theorem for function f(x)=(x^(2)-1)(x-2) on [-1,2]

Verify Rolle's theorem for the functions f(x)=(x-1)(x-2)^(2) " in " 1 le x le 2