Consider the following statements

1. The function f(x) = x² + 2 cos x is increasing in the interval (0, $$\pi$$).

2. The function $$f(x) = \ln (\sqrt {1 + {x^2}} - x)$$ is decreasing in the interval ($$-$$ $$\infty$$, $$\infty$$)

Which of the above statements is/are correct?

Consider the following statements

1. f(x) = ln x is an increasing function on (0, $$\infty$$).

2. f(x) = e^x $$-$$ x(ln x) is an increasing function on (1, $$\infty$$).

Which of the above statements is/are correct?

Consider the function $$f(x) = {\left( {{1 \over x}} \right)^{2{x^2}}}$$, where x > 0.

At what value of x does the function attain maximum value?

Consider the function $$f(x) = {\left( {{1 \over x}} \right)^{2{x^2}}}$$, where x > 0.

The maximum value of the function is