Consider the following for the two (02) items that follow: Let ABC be a triangle right-angled at B and AB+AC = 3 units.

What is the maximum area of the triangle?

Consider the following for the two (02) items that follow:
The slope of the tangent to the curve y = f(x) at (x, f(x) ) is 4 for every real number x and the curve passes through the origin.

What is the nature of the curve?

Consider the following for the two (02) items that follow:
Let the function f(x) = x ² + 9

Consider the following statements:
I. f(x) is an increasing function.
II. f(x) has local maximum at x = 0
Which of the statements given above is/are correct?

Direction : Consider the following for the items that follow :

Let f(x) = cos2x + x on [-π/2, π/2]. 

What is the greatest value of f(x)?