Application of ...

What is the slope of the tangent to the curve $$y=sin^{-1}(sin^2x)$$ at $$x=0$$ ?

Find the slope of the normal to the curve $$4x^3+6x^2-5xy-8y^2+9x+14=0$$T the point $$-2, 3$$.

A mirror in the first quadrant is in the shape of a hyperbola whose equation is xy = 1. A light source in the second quadrant emits a beam of light that hits the mirror at the point (2,1/2). If the reflected ray is parallel to the y-axis the slope of the incident beam is 

The value of $$K$$ in order that $$f(x) = \sin x - \cos x - Kx + 5$$ decreases for all positive real values of $$x$$ is given by

The function $$f(x)=\cfrac { \sin { x }  }{ x } $$ is decreasing in the interval

Consider the curve $$y = e^{2x}$$.Where does the tangent to the curve at (0, 1) meet the x-axis ? 

The approximate value of $$f(x)={ x }^{ 3 }+5{ x }^{ 2 }-7x+9=0$$ at $$x=1.1$$ is

The equation to the normal to the hyperbola $$\dfrac {x^{2}}{16} - \dfrac {y^{2}}{9} = 1$$ at $$(-4, 0)$$ is.

Let $$f(x)=2{ x }^{ 3 }-5{ x }^{ 2 }-4x+3,\cfrac { 1 }{ 2 } \le x\le 3$$. The point at which the tangent to the curve is parallel to the X-axis is

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