| 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
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
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. |
|
|
| |
Topic |
|
Interactive Math Goodies Software
Topic Locked
