Application of ...

The points of the curve $$y={ x }^{ 3 }+x-2$$ at which its tangent are parallel to the straight line $$y=4x-1$$ are

Consider the following statements:
Statement I:
$$x > \sin x$$ for all $$x > 0$$
Statement II:
$$f(x) = x - \sin x$$ is an increasing function for all $$x > 0$$
Which one of the following is correct in respect of the above statements?

The critical points of the function $$f(x)={ x }^{ 3/5 }\left( 4-x \right) ,x\in { R }^{ + }\cup \left\{ 0 \right\} $$ is _______

A point P moves such that sum of the slopes of the normal drawn from it to the hyperbola $$xy=16$$ is equal to the sum of the ordinates of the feet of the normal. Let 'P' lies on the curve C, then.
The equation of 'C' is?

$$f(x) = |x\log_{e}x|$$ monotonically decreases in

The percentage error in the surface area of a cube with edge x cm, when the edge is increased by $$11\%$$ is _________.

Let, $$f:A\rightarrow B$$ be an invertible function. If $$f(x)=2x^3+3x^2+x-1$$, then $$f'^{-1}(5)$$=

The point on the curve $$y^{2}=x$$ where tangent makes $$45^{o}$$ angle with $$x-$$axis ?

The tangent to $$\left( a{ t }^{ 2 },2at \right) $$ is perpendicular to X-axis at _____ point $$t\in R$$.

Line $$y=x$$ and curve $$y=x^2+bx+c$$ touches at $$(1, 1)$$ then __________.