Application of ...

The function $$f(x)=x-ln|2x+1|,x\epsilon \left(-100,\dfrac{-1}{2}\right)\cup \left(\dfrac{-1}{2},\dfrac{1}{2}\right)$$ is decreasing in interval

For what values of a , $$f(x) = -x^3 +4ax^2 +2x-5$$ is decreasing $$\forall$$ x

Equation of the tangent line at $$y=\dfrac{a}{4}$$ to the curve $$y\left( { x }^{ 2 }+{ a }^{ 2 } \right) ={ ax }^{ 2 }$$.

Which of the following is not always correct for the function $$f(x)$$ and $$g(x)$$ these are inverse to each other.

Solve it:-
$$y = x + \dfrac{1}{x},$$

The increasing function in $$(0,\ \pi /4)$$ is

In the interval $$\left( {7,\infty } \right),f(x) = \left| {x - 5} \right| + 2\left| {x - 7} \right|$$ is 

Let $$f :\left[ 2,4 \right] \rightarrow \left[ 3,5 \right] $$ be a bijective decreasing function, then find $$\int _{ 2 }^{ 4 }{ f(t)dt- } \int _{ 3 }^{ 5 }{ { f }^{ -1 }(t)dt. } $$

The increasing function in $$\left(0,\pi/4\right)$$ is 

If $$f(x)=\cos x+a^{2}x+b$$ is an increasing function for all values of $$x$$, then the value which $$'a'$$ can take.