If the derivative of the function$f(x) =\frac{m}{x} +2nx + 1$ vanishes at x = 2, then what is the value of m + 8n ?

What is the area included in the first quadrant between the curves y = x and y = x³ ?

If xy = 4225 where x, y are natural numbers, then what is the minimum value of x + y ?

What does the equation $x \frac{dy}{dx}-2y= 0$ represent ?