- #1
razmtaz
- 25
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Homework Statement
let f = [itex]\mu[/itex]ex
let 0 < [itex]\mu[/itex] < 1/e
Show that f has two fixed points q and p with q < p
Homework Equations
a fixed point p is a point such that f(p) = p
The Attempt at a Solution
solving f(x) = x:
f(x) - x = 0
[itex]\mu[/itex]ex - x = 0
Now I want to take logarithms but ln(0) is undefined.
This is the 'normal', algebraic way of solving for fixed points. Is there another way to solve for fixed points? I tried looking at the derivatives based on a suggestion but f'(x) = f(x) which doesn't tell me very much, and I also tried iterating the function, but it just seems to get messy (ie f(f(x)) = [itex]\mu[/itex]e[itex]\mu[/itex]ex )
Any suggestions for finding fixed points would be helpful. I would prefer not to use the Newton-raphson method to find a root of g(x) = f(x) - x, so if there are any other strategies please let me know