Application Of Derivatives - Calculus - Mathematics Previous Year Questions

The sides of an equilateral triangle are increasing at the rate of \(4 \mathrm{~cm} / \mathrm{sec}\). The rate at which its area is increasing, when the side is \(14 \mathrm{~cm}\)

The interval in which the function \(f(x)=x^3-6 x^2+9 x+10\) is increasing in

If the side of a cube is increased by \(5 \%\), then the surface area of a cube is increased by

If the curves \(2 x=y^2\) and \(2 x y=K\) intersect perpendicularly, then the value of \(K^2\) is

The maximum value of \(\frac{\log _e x}{x}\), if \(x>0\) is

A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of \(t=4\) is \(k\), then the value of \(5 k\) is

The cost and revenue functions of a product are given by \(c(x)=20 x+4000\) and \(R(x)=60 x+2000\) respectively, where \(\mathrm{x}\) is the number of items produced and sold. The value of \(x\) to earn profit is

The function \(f(x)=x^2-2 x\) is strictly decreasing in the interval

The maximum slope of the curve \(y=-x^3+3 x^2+2 x-27\) is

The function \(f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100\) is strictly

The coordinates of the point on the \(\sqrt{x}+\sqrt{y}=6\) at which the tangent is equally inclined to the axes is

The function \(f(x)=\log (1+x)-\frac{2 x}{2+x}\) is increasing on

The distance '\(s\)' in meters travelled by a particle in '\(t\)' seconds is given by \(s=\frac{2 t^3}{3}-18 t+\frac{5}{3}\). The acceleration when the particle comes to rest is :