Originally Posted by

**coe236** Use Newtons method to find the two solutions of e^x=5*x to three decimal places.

*Newtons Method: X(n+1) = Xn - f(Xn)/f'(Xn)*

I just dont understand how you would set this up. Do you set both the approximations equal to each other to solve or do you solve them individually and keep checking?

Hello,

1. make a rough sketch: You'll notice that there are 2 points of intersection thus

2. the equation $\displaystyle e^x-5x = 0$ have 2 solutions.

3. consider the function $\displaystyle f(x) = e^x-5x~\implies~f'(x) = e^x-5$

then you have:

$\displaystyle x_{n+1}=x_{n}-\frac{e^{x_n}-5x_n}{e^{x_n}-5}$

Now use your calculator: Code:

start: 0 2
2. step: 0.25 3.092876765
3. step: 0.25915... 2.70696...
.
.
answer: 0.259171101.. 2.542641358...