1. ## bisection method (question)

At each n =1,2,3,4,... the table replaces either a(n) or b(n) by the value of x(n) that is in the previous row. The problem is, sometimes x(n) replaces a(n) in the next row, and sometimes x(n) replaces b(n) in the next row. So how would I decide whether to replace a(n) or b(n)?

for example, in row 2(n=2), b(n) is replaced by x(n)=0.26. If i where to instead replace a(n) by x(n)=0.26, would it still be correct?

2. This there an associated function here? Might be helpful.

Anyhow. You have a and b and the midpoint x = (a+b)/2 where a < x < b.

So you find f(a), f(x), f(b). Look at there signs.

Lets say f(a) = +ve, f(x) = -ve, f(b) = -ve.

Always point the new interval to be the 2 functions that differ in signs. In this case your new interval will be (a,x) not (x,b)

Do you follow?

3. thanks, I got it now. The function is $f(x)=3x-e^(-x)$

Do you have perhaps a website or something that explains what you just mentioned? I get what you said, but i just want to read up further on it

4. I do have a website