Doubt

[Halflife]

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[Asd1995]

It means f'(x)*f(x)=0 for some x, which is true.

Consider f(x)<0 for all x. This implies the graph tapers off to some negative value as x approaches minus infinity. So derivative will tend to 0 there which will make product 0

Similarly consider f(X)>0 for all x. Graph tapers off at x=infinity, by the same argument the product vanishes to 0.

In other cases f(x)=0 for some x.

[Halflife]

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[Abhitesh]

How is f'(x)*f(x)=0.

Also strictly decreasing function would imply Df(x)<0 FOR ALL x in R.