Application of ...

The slope of the curve $$\displaystyle y=\sin x+\cos ^{2}x $$ is zero at the point where -

The slope of the tangent to the curve $$\displaystyle y=\sin x$$ at point $$(0, 0)$$ is

If tangent at a point of the curve $$y = f(x)$$ is perpendicular to $$2x - 3y = 5$$ then at that point $$\displaystyle \dfrac{dy}{dx}$$ equals

The inclination of the tangent w.r.t. $$x$$ - axis to the curve $$\displaystyle x^{2}+2y=8x-7$$ at the point $$x = 5$$ is

At what point the tangent to the curve $$\displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a}$$ is perpendicular to the $$x$$ - axis

The slope of the tangent to the curve $$\displaystyle y=-x^{3}+3x^{2}+9x-27$$ is maximum when x equals.

The line $$y = x + 1$$ is a tangent to the curve $$ y^2 = 4x$$ at the point.

The rate of change of the area of a circle with respect to its radius $$r$$ at $$r = 6 cm$$ is.

The side of a square sheet is increasing at the rate of $$4 cm$$ per minute. The rate by which the area increasing when the side is $$8 cm$$ long is.

The slope of the normal to the curve $$y = 2x^2+ 3 \sin x$$ at $$x = 0$$ is.