Continuity and ...

Verify Rolle's theorem the function $$\displaystyle f(x)=x^{3}-4x $$  on  $$ [-2,2].$$ If you think it is applicable in the given interval then find the stationary point ?

Verify the Rolle's theorem for the function $$\displaystyle f(x)=x^{2}$$ in $$(-1,1)$$

Verify the Rolle's theorem for the function $$\displaystyle f(x)=x^{2}-3x+2$$ on the interval[1,2]

Verify Rolle's theorem for the function $$\displaystyle f(x)=10x-x^{2}$$ in the interval [0,10]

If $$y = \displaystyle (\tan x)^{\log x}$$, then $$\cfrac{dy}{dx} = $$

Verify Lagrange's mean value for the function $$f(x)=\displaystyle \sin x$$ in $$\displaystyle \left [ 0,\frac{\pi }{2} \right ]$$

Find 'c' of the mean value theorem, if $$\displaystyle f(x)=x(x-1)(x-2);a=0, b=1/2$$

Discuss the applicapibility of Rolle's Theorem to the function $$\displaystyle f(x)=x^{2/3}$$ in (-1,1).

If $$\displaystyle x=2 \cos t-cos 2t, y=2\sin t-\sin 2t,$$ find the value of $$dy/dx$$.

The function $$f(x) = \displaystyle \sin ^{-1}(\cos x)is :-$$