Continuity and ...

If Rolle's therorem holds for $$f(x)=x\left( { x }^{ 2 }+ax+b \right) +2atx=\frac { 1 }{ 2 } $$in the interval (-1 , 1), then which of the following (S) is/are corect? 

Let $$f\left( x \right)$$ be non-constant differentiable function for all real $$x$$ and $$f\left( x \right) =f\left( 1-x \right) $$. Then Rolle's theorem is not applicable for $$f\left( x \right)$$ on

in $$\left[ a,b \right] $$ and differentiable in (a,b) then the value of 'c' for the pair of functions
$$f\left( x \right) \sqrt { x, } \phi \left( x \right) =\dfrac { 1 }{ \sqrt { x }  } $$ is

Let f(x) be a polynomial in x. Then the second derivation of f$$\left( { e }^{ x } \right) $$, is:

Let f be a differentiable function satisfying the condition $$f(\dfrac{x}{y}) = \dfrac{f(x)}{f (y)}$$ for all $$x, y ( \neq 0) \epsilon R, f(y) \neq 0$$. If $$f' (1) =2 $$, then $$f ' (x) $$ is equal to

Solve  $$ x ^ { 4 } \left( \dfrac { d y } { d x } \right) ^ { 2 } - x \dfrac { d y } { d x } - y = 0$$

If 

$$\dfrac{d}{dx}$$ { $$\cot^{-1} \dfrac{\sqrt{1+x} - \sqrt{1-x}}{\sqrt{1+x} - \sqrt{1-x}}$$ } =

If $$f(x)$$ is a four times differentiable even function, then $$\int_{-3}^{3}(x^{3}f(x)+xf''''(x)+2)dx$$    is equal to 

Let f, g and h are function differentiable on some open interval around $$0$$ and satisfy the equations $$f'=2f^2gh+\dfrac{1}{gh}, f(0)=1, g'=fg^2h+\dfrac{4}{fh}, g(0)=1$$ and $$h'=3fgh^2+\dfrac{1}{fg}, h(0)=1$$. The function f is given by?