Application of ...

$$f(x)=\cfrac{x}{5}+\cfrac{5}{x}$$ is increaing in

The complex number $$\frac{(-\sqrt 3 + 3i)(1-i)}{(3 + \sqrt 3i) (i) (\sqrt 3 + \sqrt 3i)}$$ when represented in the Argand diagram is 

If the line $$ax+y=c$$, touches both the curves $${x}^{2}+{y}^{2}=1$$ and $${y}^{2}=4\sqrt{2}x$$, then $$\left| c \right| $$ is equal to:

Let $$f"(x) > 0$$ and $$\phi (x) = f(x) + f(2 - x) , x \in (0,2)$$ be a function, then the function $$\phi (x)$$ is

The slope of the tangent to the curve $$x=t^2+3t-8, y=2t^2-2t-5$$ at point $$(2, -1)$$ is

At what points the slope of the tangent to the curve $$x^2+y^2-2x-3=0$$ is zero?

The point on the curve $$y=12x-x^2$$, where the slope of the tangent is zero will be

The slope of the tangent to the curve $$x=3t^2+1, y=t^3-1$$ at $$x=1$$ is

Mark the correct alternative of the following.
The point on the curve $$9y^2=x^3$$, where the normal to the curve makes equal intercepts with the axes is?

Mark the correct alternative of the following.
The line $$y=mx+1$$ is a tangent to the curve $$y^2=4x$$, if the value of m is?