Application of ...

The function f(x) is 

If $$ f(x) = \displaystyle \int_{1}^{x} e^{t^2/2}(1-t^2)dt, $$ then $$\dfrac{d}{dx} f(x) $$ at x=1 is 

The tangent to the curve $$y = e^{x}$$ drawn at the point $$(c, e^{c})$$ intersects the line joining the points $$(c-1, e^{c-1})$$ and $$(c+1, e^{c+1})$$

Number of critical point for $$y=f(x)$$ for $$x \in [0,2]$$

If the line ax +by + c = 0 is a normal to the curve xy = 1, then 

The equation of the curves through the point $$(1,0)$$ and whose slope is $$ \dfrac{y -1}{x^{2} + x} $$ is

The point of the curve $$ y^2 = x$$ where the tangent makes an angle of $$ \frac { \pi}{4} $$ with x-axis is 

The abscissa of the point on the curve $$ 3y=6x- 5x^3 $$ the normal at which passes through origin is :

The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is :

The curve $$ y=x^{\frac{1}{5}} $$ has at $$ (0,0) $$