Solving Newton's Method for f(x) = 0: Step-by-Step

[EL ALEM]

Homework Statement

Nother Q for today:
Let f(x)= (1/x)^x - x
(a)show that f(x)=0 has a solution
(b)show that there is only one solution to f(x)=0
(c)use Newton's Method to find the second approximation x2 of the solution to f(x) =
0 using the initial approximation x1 = 1/2

Homework Equations

The Attempt at a Solution

I know how to do part C just need a little kick in the right direction for the first part.

(1/x)^x - x = 0
(1/x)^x = x
xln(1/x) = lnx

 

[earlh]

x \log(1/x) = \log(x)

Remember what \log(a/b) equals to? Break the pieces out.

 

[HallsofIvy]

How about the simple fact that 1 to any power is 1?

 

[EL ALEM]

I already got it, it was late and I wasn't thinking straight, thanks for the replies though.