Thread: Calculus Query
View Single Post
  #13   Spotlight this post!  
Unread 17-10-2005, 20:37
Unsung FIRST Hero
Karthik Karthik is offline
VEX Robotics GDC Chairman
no team
Team Role: Mentor
 
Join Date: Apr 2002
Rookie Year: 1998
Location: Toronto, Ontario, Canada
Posts: 2,342
Karthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond reputeKarthik has a reputation beyond repute
Re: Calculus Query

Quote:
Originally Posted by phrontist
I meant (and said) inverse, not reciprocal. This isn't an assignment, just something that occured to me during my endless and tedious BC Caluclus (anyone else have Early Transcendentals?) homework.

I've been trying to approach the problem visually, the inverse of a function being that function "mirrored" about the line y=x. I think perhaps this is needlessly painful, I'm going to try some algerbraic manipulation of the definition of the derivative...

My guess is that no such function exists, but I wonder if there is an elegant proof of that.
The following fact will lead you in the right direction.

Let f be a function that is differentialable on an interval I. Suppose that f has a defined inverse function, called g.

Using the defintion of an inverse, and the chain rule, it can be shown that

g'(x) = 1/f'(g(x)), where f'(g(x)) != 0

This should help with you algebraic manipulation.
__________________
:: Karthik Kanagasabapathy ::
"Enthusiasm is one of the most powerful engines of success. When you do a thing, do it with all your might. Put your whole soul into it. Stamp it with your own personality. Be active, be energetic, be enthusiastic and faithful and you will accomplish your object. Nothing great was ever achieved without enthusiasm" -- R.W. Emerson
My TEDx Talk - The Subtle Secrets of Success
Full disclosure: I work for IFI and VEX Robotics, and am the Chairman of the VEX Robotics and VEX IQ Game Design Committees
.
Reply With Quote