Application of ...

If the straight line $$ y -2x +1=0$$ is the tangent to the curve $$xy+ax+by=0$$ at $$x=1, $$ then the values of $$a$$ and $$b$$ are respectively :

The point on the curve $$y = 5 + x - x^{2}$$ at which the normal makes equal intercepts is

If the angle between the curves $$ y = 2^x $$ and $$ y=3^x $$ is $$ \alpha, $$ then the value of $$ \tan \alpha $$ is equal to :

The equation of the tangent to the curve $$\sqrt {\dfrac {x}{a}} + \sqrt {\dfrac {y}{b}} = 1$$ at the point $$(x_{1}, y_{1})$$ is $$\dfrac {x}{\sqrt {ax_{1}}} + \dfrac {y}{\sqrt {by_{1}}} = k$$. Then, the value of $$k$$ is

The slope of the normal to the curve $$y = x^2 - \dfrac{1}{x^2}$$ at $$(-1, 0) $$ is 

The slope of the tangent to the curve $$y=3{ x }^{ 2 }-5x+6$$ at $$\left( 1,4 \right) $$ is

The function $$f(x) = 2x^3 - 15 x^2 + 36 x + 6$$ is strictly decreasing in the interval

A normal to parabola, whose inclination is $$30^o$$, cuts it again at an angle of.

If the slope of the tangent to the curve $$y=a{ x }^{ 3 }+bx+4$$ at $$(2,14) = 21$$, then the values of $$a$$ and $$b$$ are respectively

Let $$\quad f(x)+2f(1-x)={ x }^{ 2 }+2\forall x\in R\quad $$ then the interval in which $$f(x)$$ increases is