Application of Derivatives

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
travels along OB with a speed of 3 km/h. The
rate at which the shortest distance between X
a...

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

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

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