For the following three (03) items:
Consider the function f(x) = x|x|

Consider the following statements:

I. The function is increasing in the interval (-∞,∞),

II. The function is differentiable at x = 0

Which of the statements given above is/are correct?

For the following two (02) items:
Consider the function
$f(x)=\frac{x}{1-x}(x>0,x\ne 1)$

What is $\frac{f(x)}{f(x+1)}$ equal to?

For the following two (02) items:
Consider the function
$f(x)=\frac{x}{1-x}(x>0,x\ne 1)$

What is $ (1-x)f(\sqrt{x})+xf(\sqrt{x}+1)$ equal to?
 

For the following three (03) items:
Let $y=f(x)=\frac{x\sin ^{-1}x}{\sqrt{1-x^{2}}}+\ln \sqrt{1-x^{2}}.$

What is the slope of the tangent to the curve y = f(x) at x = 0.5