Where does the tangent to the curve y = e^x at the point (0, 1) meet x-axis?

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 the condition that f(x) = x³ + x² + kx has no local extremum?