Direction : Consider the following for the items that follow :

Let f(x) = cos2x + x on [-π/2, π/2]. 

What is the least value of f(x)? 

Direction : Consider the following for the items that follow :

The area bounded by the parabola y² = kx and the line x = k, where k > 0, is 4/3 square units.

What is the value of k? 

Direction : Consider the following for the items that follow :

The area bounded by the parabola y² = kx and the line x = k, where k > 0, is 4/3 square units.

What is the area of the parabola bounded by the latus rectum? 

Direction : Consider the following for the items that follow :

Let ydx + (x - y³)dy = 0 be a differential equation.  

What are the order and degree respectively of the differential equation?