Application of ...

The equation of normal of $$x^2+y^2-2x+4y-5=0$$ at $$(2,\,1)$$ is

The coordinates of the point P on the curve $$x = a(\theta + \sin \theta), y = a(1 - \cos \theta)$$ where the tangent is inclined at an angle $$\dfrac {\pi}{4}$$ to the x-axis, are

The slope of the tangent to the curve $$x=3t^2+1, y=t^3-1$$ at $$x=1$$ is 

The function $$f(x)=\frac{x}{3}+\frac{3}{x}$$ decreaes in the interval.

Find the equation of the quadratic function $$f$$ whose graph increases over the interval $$(-\infty, -2)$$ and decreases over the interval $$(-2,+\infty)$$, $$f(0)=23$$ and $$f(1)=8$$

The focal length of a mirror is given by $$\displaystyle \frac{2}{f}\, =\, \displaystyle \frac{1}{v}\, -\, \displaystyle \frac{1}{u}$$. In finding the values of u and v, the errors are equal and equal to 'p'. The the relative error in f is

Suppose that $$f$$ is a polynomial of degree $$3$$ and that $$f''(x)\neq 0$$ at any of the stationary point. Then

Let $$f:R\rightarrow R$$ be a differentiable function for all values of $$x$$ and has the peoperty that $$f(x)$$ and $$f'(x)$$ have opposite signs for all values of $$x$$. Then,

The function $$f(x) = x^2$$ is decreasing in

Identify the correct statements
(a) Every constant function is an increasing function.
(b) Every constant function is a decreasing function.
(c) Every identify function is an increasing function.
(d) Every identify function is a decreasing function.