Math Help - Bisection method

1. Bisection method

Use the bisection method to find the root of:

x = e^-x

2. Read "The Method" from here.

Bisection method - Wikipedia, the free encyclopedia

Choose $a=-1$ and $b=1$ as endpoints for the first iteration

Now find c the midpoint that bisects the interal. $c = \frac{b+a}{2} = \frac{1-1}{2} = 0$

find $f(a), f(b)$ and $f(c)$

You will find

$f(a) = f(-1)<0$

$f(b) = f(1) >0$

$f(c) = f(0) <0$

So now as $f(c) < 0$ choose it and $f(b) > 0$ to be the new interval as they have opposite signs as so on. The interval will get smaller and converge on the solution.