Application of ...

Point on the curve $$f(x)=\dfrac{x}{1-x^{2}}$$ where the tangent is inclined at an angle of $$\dfrac{\pi }{4}$$ ot the x-axis are 

The abscissa of points P and Q in the curve $$y = e^{x}+e^{-x}$$ such that tangents at P and Q make $$60^{o}$$ with the x-axis

The x-intercept of the tangent at any arbitrary point of the curve $$\dfrac{a}{x^{2}}+\dfrac{b}{y^{2}}=1$$ is proportion to

If the tangent at any point $$P(4m^{2}, 8m^{3})$$ of $$x^{3}-y^{3}=0$$ is also a normal to the curve  $$x^{3}-y^{3}=0$$ , then value of m is

Consider the following statement is $$S$$ and $$R$$ 
$$S$$. Both $$\sin x$$ and $$\cos x$$ are decreasing function in the interval $$\left(\dfrac {\pi}{2}, \pi \right)$$
$$R:$$ If a differentiable function decreases in an interval $$(a, b)$$ then its derivative also decreases in $$(a, b)$$, which of the following is true?

The normal to the curve $$x = a (\cos 0 + 0\sin 0), y= a (\sin 0- 0\cos 0)$$ at any point 0 is such that

The slope of the tangent to the curve $$y = f(x)$$ at $$\left [ x, f(x) \right ]$$ is 2x + 1. If the curve passes through the point (1, 2)then the area bounded by the curve, the x-axis and the line x = 1 is

The point(s) on the curve $$y^{3} + 3x^{2} = 12y,$$ where the tangent is vertical, is (are)

A curve passes through $$(2,1)$$ and is such that the square of the ordinate is twice the contained by the abscissa and the intercept of the normal. Then the equation of curve is

The curve for which the ratio of the length of the segment by any tangent on the $$Y-$$axis to the length of the radius vector is constant $$(K)$$, is