ISI Entrance question

[XIPP]

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!

[Bankelal]

Yes you are right and these two possibilities are considered!

1. f(x)>0 and f'(x)<0 and 
2. f(x)<0 and f'(x)>0, right?

For 1., f(x) is a decreasing function if f(x)>0,

thus |f(x)| is a decreasing function, wrt 2.  as |f(x)| >0 , for f(x)<0

On Tue, Dec 3, 2013 at 8:57 AM, XIPP [via Discussion forum] <[hidden email]> wrote:

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!

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[don123]

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