Author 
Topic 

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
Advanced Member
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 Value
f(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
Advanced Member
USA
9116 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
Advanced Member
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 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. 


tkhunny
Advanced Member
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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