Application of ...

Two lines drawn through the point $$A ( 4,0 )$$  divide the area bounded by the curve $$y = \sqrt { 2 } \sin ( \pi x / 4 )$$  and  $$x$$ - axis between the lines $$x = 2$$  and   $$x = 4$$  into three equal parts. Sum of the slopes of the drawn lines is:

If $$- 4 \leq x \leq 4$$ then critical points of $$f ( x ) = x ^ { 2 } - 6 | x | + 4$$ are 

The number of critical points of the function $$f(x)=|x-1||x-2|$$ is 

$$f(x)=\dfrac{x}{5}+\dfrac{4}{x}(x\neq 0)$$ in increasing in

The tangent to the curve $$2a^2y=x^3-3ax^2$$ is parallel to the x-axis at the points

The line $$3x-4y=0$$

If $$x-2y+k=0$$ is a common tangent to $$\displaystyle{ y }^{ 2 }=4x\quad \& \frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { 3 } } =1\left( a>\sqrt { 3 }  \right)  $$, then the value of a, k and other common tangent are given by

The tangent at any point of the curve $$x={ at }^{ 3 },y={ at }^{ 4 }$$ divides the abscissa of the point of contact in the ratio

If the slope of one of the lines represented $${a^3}{x^2} + 2hxy + {b^3}{y^2} = 0$$ be the square of the other, then $$ab(a+b)$$ is equal to:

Slope of tangent to the circle $$( x - r ) ^ { 2 } + y ^ { 2 } = r ^ { 2 }$$ at the point $$( x , y )$$ lying on the circle is