In which of the following functions is Rolles theorem applicable? `(a)f(x)={x ,0lt=x<1 0,x=1on[0,1]` `(b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0)` `(c)f(x)=(x^2-x-6)/(x-1)on[-2,3]` `(d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]`

In which of the following function Rolle's theorem is applicable ?

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]

Rolle’s theorem can not applicable for :

Verify Rolle's theorem for each of the following functions on indicated intervals; f(x)=sin^2x on 0lexlepi f(x)=sinx+cosx-1 on [0,pi/2] f(x)=sinx-sin2x on [0,pi]

Consider a function f(x) = ln ((x^2 + alpha)/(7x)) . If for the given function, Rolle's theorem is applicable in [3,4] at a point C then find f'' (C)

Verify Rolle's theorem for the following functions in the given intervals. f(x) = x(x-4)^(2) in the interval [0,4].

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sin 3x in the interval [0,pi] .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sinx + cos x in the interval [0 , pi//2] .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sin^(2) x in the interval [0,pi] .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = x^(2) in the interval [-2,2] .