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kylek1151
Senior Member

USA
21 Posts

 Posted - 10/10/2007 :  18:23:21 I have sort of a theory question on a assignment that is giving me a bit of trouble. It is stated as follows:Suppose that u=g(x) is differentiable at x=-5, y=f(u) is differentiable at u=g(-5) and (f°g)(-5) is negative. What can you say about the values of g(-5) and f'(g(-5))? So far all I can think of is that both values exist. Any push in the right direction on this one would be greatly appreciated.

tkhunny

USA
1001 Posts

 Posted - 10/11/2007 :  08:12:50 I'm not quite sure what they are getting at, but my favorite answer would be:g(-5) = u -- A Real Valuef(u) = Some Real Value - a constant.f'(u) is the derivative of a constant and is zero.Nothing like a notational deficiency.

kylek1151
Senior Member

USA
21 Posts

 Posted - 10/11/2007 :  13:36:33 Ah yes, I see the derivative of f'(g(-5)) must be 0. That is probably what they are looking for on that one. Thanks. I wonder what they are looking for me to say about g(-5) though. Maybe just that it is a real value?

Subhotosh Khan

USA
9114 Posts

 Posted - 10/12/2007 :  06:59:38 quote:Originally posted by kylek1151 I wonder what they are looking for me to say about g(-5) though. Maybe just that it is a real value?Since g(x) is differentiable at x = -5, it must exist (defined).

HallsofIvy

USA
78 Posts

 Posted - 10/12/2007 :  10:14:40 I would have interpreted f'(g(5)) to mean the derivative of f, evaluated at g(5).

kylek1151
Senior Member

USA
21 Posts

 Posted - 10/12/2007 :  13:44:26 quote:Originally posted by HallsofIvyI would have interpreted f'(g(5)) to mean the derivative of f, evaluated at g(5).Yea, it is. I thought about it more and you can't say that f'(g(-5)) would be 0. I already turned in the assignment though. I guess I got that one wrong. Also the question asked what we can say about g'(-5), not g(-5). The paper was faded and I couldn't see the ' lol. Oh well, I'll count that one as a total loss I guess. Still interested to see if anyone else has a answer for this one.

tkhunny

USA
1001 Posts

 Posted - 10/12/2007 :  14:52:17 I would argue it if it is marked wrong. Unless you specifically disussed that notation to mean what Halls has taken it to mean, then it is inherently ambiguous.
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