Consider the following statements in respect of the function f(x) = x + $\rm \frac{1}{x}$:

1. The local maximum value of f(x) is less than its local minimum value.

2. The local maximum value of f(x) occurs at x = 1.

Which of the above statements is/are correct?

What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?

What is $\rm \int \frac{dx}{x(x^2 + 1)}$ equal to?

What is the derivative of $\rm e^{e^x}$ with respect to e^x?