Using Newtons Method to find intercept of 2 curves?

Question

I know how to use Newtons Method to find the intercept of the x-axis, but how do you use it to find the intercept of 2 curves? 
For example, use Newtons Method to find the approximate x-coordinates of all intersections for Y = e^(-x) and y = ln(x).

Newtons Method.... X(n+1) = Xn - ( f (Xn) / f '(Xn))

Please show me step-by-step - thanks

intc_escapee · Accepted Answer

f(x) = ln(x) - 1/e^x
f'(x) = 1/x + 1/e^(x)
X(n+1) = Xn - ( f (Xn) / f '(Xn))

Use an initial estimate of 1
Xn+1 ..... Xn ......... f(Xn) ..... f'(Xn)
1.2689 .. 1.0000 .. -0.3679 .. 1.3679
1.3091 .. 1.2689 .. -0.0429 .. 1.0692
1.3098 .. 1.3091 .. -0.0007 .. 1.0339
1.3098 .. 1.3098 .. 0.0000 .. 1.0333

Answer: x ≈ 1.3098

efqy · Answer

Y = y if Y - y = 0.

i.e. use newton's method to find a root of exp(-x) - ln(x)

1 would be a reasonable starting point.

Using Newtons Method to find intercept of 2 curves?

2 Answers