The length and breadth of a rectangle are $x_{x \mathrm{~cm}}$ and $y \mathrm{~cm}$ respectively. If the length decreases at the rate of $5 \mathrm{~cm} /$ minute and the breadth increases at the rate of $3 \mathrm{~cm} /$ minute, then the rates of change of the perimeter and area respectively when the length is 5 cm and breadth is 2 cm , are

The maximum value of $x^{2 / 3}+(x-2)^{2 / 3}$ is

The point on the curve $4 y^2-4 y+2 x-1=0$ at which the tangent becomes parallel to Y -axis is

A particle moves along a curve $y=\frac{2 x^3-1}{3}$. The points on the curve at which the $y$ co-ordinate is changing 18 times the $x$ co-ordinate are