ISI Entrance question

Posted by XIPP on Dec 03, 2013; 3:12am
URL: http://discussion-forum.276.s1.nabble.com/ISI-Entrance-question-tp7584292.html

Question from ISI MSQE 2007:(SEE Q29 of math part.)

Given that f is a real-valued differentiable function such that f(x)f′(x)<0 for all
real x, it follows that :
Ans.(According to Amit Sir's solution:solution)
|f(x)| is a decreasing function .

Is the question asks to work with f(x)*f′(x)<0 or is there some typo? If f(x)*f′(x)<0 is true, I think we should consider two possibilities:
1. f(x)>0 and f'(x)<0 and
2. f(x)<0 and f'(x)>0, right?

Aditya, please help again!