Application of ...

Find the equation of a line passing through $$(-2,3)$$ and parallel to tangent at origin for the circle $$\displaystyle x^{2}+y^{2}+x-y=0$$

 Stationary point of $$\displaystyle \mathrm{y}=\frac{\log \mathrm{x}}{\mathrm{x}}(\mathrm{x}>0)$$ is

I: lf $$\mathrm{f}'(\mathrm{a})<0$$ then the function $$\mathrm{f}$$ is decreasing at $$\mathrm{x}=\mathrm{a}$$
II: lf $$\mathrm{f}$$ is decreasing at $$\mathrm{x}=\mathrm{a}$$ then $$\mathrm{f}'(\mathrm{a})<0$$ 
Which of the above statements are true ?

The slope of tangent to the curve $$y=\int_{0}^{x}\displaystyle \frac{dx}{1+x^{3}}$$ at the point where $$x=1$$ is

The value of $$\mathrm{x}$$ at which $$\mathrm{f}(\mathrm{x})=$$ cosx is stationary are given by

The number of stationary points of $$\mathrm{f}(\mathrm{x})=\cos \mathrm{x}$$ in $$[0, 2{\pi}]$$ are

The curve $$\displaystyle y-e^{xy}+x=0$$ has a vertical tangent at

The stationary point of $$\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-10\mathrm{x}+43$$ is

The point on the curve $$\displaystyle y=x^{2}-3x+2$$ at which the tangent is perpendicular to the line $$y = x$$ is -

If tangent to curve at a point is perpendicular to $$x$$ - axis then at that point -