Application of Derivatives · Mathematics · COMEDK

The slope of the tangent to the curve, $$y=x^2-x y$$ at $$\left(1, \frac{1}{2}\right)$$ is

Let $$f(x)=a+(x-4)^{\frac{4}{9}}$$, then minima of $$f(x)$$ is

The function $$f(x)=\frac{x}{2}+\frac{2}{x}$$ has a local minimum at

$$ f(x)=2 x-\tan ^{-1} x-\log (x+\sqrt{x^2+1}) \text { is monotonically increasing, when } $$

The altitude of a cone is $$20 \mathrm{~cm}$$ and its semi vertical angle is $$30^{\circ}$$. If the semi vertical angle is increasing at the rate of $...

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

If the tangent to the curve $$xy + ax + by = 0$$ at (1, 1) is inclined at an angle $${\tan ^{ - 1}}2$$ with X-axis, then

Let $$f(x) = a - {(x - 3)^{8/9}}$$, then maxima of $$f(x)$$ is

The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7x^2+15$$ is

Find the maximum value of $$f(x) = {1 \over {4{x^2} + 2x + 1}}$$.

The point on the curve $$y^2=x$$, the tangent at which makes an angle 45$$^\circ$$ with X-axis is

The length of the subtangent to the curve $${x^2}{y^2} = {a^4}$$ at $$( - a,a)$$ is

The range in which $$y = - {x^2} + 6x - 3$$ is increasing, is

OA and OB are two roads enclosing an angle of 120$$^\circ$$. X and Y start from O at the same time. X travels along OA with a speed of 4 km/h and Y tr...