Application of ...

The entire graph of the equation $$y=x^{2}+kx-x+9$$ is strictly above the $$x-$$axis if and only if : 

If $$y=e^{4x}+2e^{-x}$$ satisfied the equation $$\dfrac{d^{3}y}{dx^{3}}+A\dfrac{dy}{dx}+By=0$$ then value of $$|A+B|$$ is 

Let $$f(x)$$ be a differentiate function and $$f(\alpha)=f(\beta)=0(\alpha < \beta)$$, then in the interval $$(\alpha, \beta)$$.

If $$f(x) = g(x) (x - \lambda)^2 \,$$ and $$\, g (\lambda)$$, where  $$0 < x \le 1$$, then in this interval 

Let $$h(x) = f(x) - (f (x) )^2 + (f(x))^3$$ for every real number $$x$$, then 

If $$f'\left( x \right) = \sqrt {2{x^2} - 1} $$ and $$y = f\left( {{x^2}} \right)$$, then $$\frac{{dy}}{{dx}}$$ at $$x = 1$$ is equal to 

Find the slope of the normal to the curve $$2x^{2} - xy + 3y^{2} = 18$$ at $$(3,1)$$.

Area of the triangle formed by the tangent at $$x=2$$ on the curve $$y= \dfrac{8}{4+x^2}$$ with the coordinate axes is (in sq. units)

The curve $$y = ax^3 + bx^2 + cx + 8$$ touches $$x-$$ axis at $$P(-2, 0)$$ and cuts $$y-$$ axis at a point $$Q$$ where its gradient is $$3$$. The values of $$a, b, c$$ are respectively ?

The curve satisfying D.E $$y dx - (x+3{y}^{2})dy=0$$ and passing through the point $$(1,1)$$ also passes through the point: