Application of ...

If $$f(x)=min(|x|^{2}-5|x|,1)$$ then $$f(x)$$ is non differentiable at $$\lambda$$ points, then $$\lambda+13$$ equals

Find the angle between tangent of the curve $$y = (x + 1) (x - 3)$$ at the point where it cuts the axis of $$x$$.

If the curves $$y^2 = 4ax$$ and $$xy = c^2$$ cut orthogonally then $$\dfrac{c^4}{a^4} =$$

Number of critical points of the function $$\displaystyle f\left( x \right) =\dfrac { 2 }{ 3 } \sqrt { { x }^{ 3 } } -\dfrac { x }{ 2 } +\int _{ 1 }^{ x }{ \left( \dfrac { 1 }{ 2 } +\dfrac { 1 }{ 2 } \cos { 2t } -\sqrt { t }  \right)  } dt$$ which lie in the interval $$\left[ -2\pi ,2\pi  \right] $$ is:

The equation of the tangent to the curve $$y = b{e^{ -\dfrac{x}{a}}}$$ at a point , where $$x=0$$ is 

The function $$y = \dfrac{2x^2 - 1}{x^4}$$ is

The equation of the curve passing through $$(1,3)$$ whose slope at any point $$(x,y)$$ on it is  $$\dfrac { y }{ { x }^{ 2 } }$$ is given by

An equation of the tangent to the curve $$y=x^{4}$$ from the point $$(2,0)$$ not on the curve is:

Let $$f:R\rightarrow  R$$  be a function defined by $$f\left(x\right)=Min \left\{x+1, \left|x\right|+1\right\}$$. Then which of the following is true?

Find the points on the ellipse $$\dfrac{{{x^2}}}{4} + \dfrac{{{y^2}}}{9}=1$$ , on which the normals are parallel to the line $$3x-y=1$$.