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 Pre-Calculus and Calculus
 Differentiation question
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kylek1151
Senior Member

USA
21 Posts

Posted - 10/10/2007 :  18:23:21  Show Profile
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 (fg)(-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.
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tkhunny
Advanced Member

USA
1001 Posts

Posted - 10/11/2007 :  08:12:50  Show Profile
I'm not quite sure what they are getting at, but my favorite answer would be:

g(-5) = u -- A Real Value

f(u) = Some Real Value - a constant.

f'(u) is the derivative of a constant and is zero.

Nothing like a notational deficiency.
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kylek1151
Senior Member

USA
21 Posts

Posted - 10/11/2007 :  13:36:33  Show Profile
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?
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 10/12/2007 :  06:59:38  Show Profile
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).
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HallsofIvy
Advanced Member

USA
78 Posts

Posted - 10/12/2007 :  10:14:40  Show Profile
I would have interpreted f'(g(5)) to mean the derivative of f, evaluated at g(5).
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kylek1151
Senior Member

USA
21 Posts

Posted - 10/12/2007 :  13:44:26  Show Profile
quote:
Originally posted by HallsofIvy

I 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.
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tkhunny
Advanced Member

USA
1001 Posts

Posted - 10/12/2007 :  14:52:17  Show Profile
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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