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# ... watch

1. ...
2. the normally the q will specify either the number of times you have to do it or the accuracythe answer has to be to
3. ...
4. ye just go with the third one then
5. (Original post by Mathsturbator.)
f(x) = 6x - 3^x

The equation f(x) = 0 has a root between x = 2 and x = 3. Starting with the interval [2,3] use interval bisection three times to give an approximation to this root.

My working (I have omitted d.p. mentions):

Edit: TSR screwed up my neat table.

a f(a) b f(b) (a+b)/2 f((a+b)/2)
2 3 3 -9 2.5 -0.588
2 3 2.5 -0.588 2.25 1.655
2.25 1.655 2.5 -0.588 2.375 0.662

Now that I have used interval bisection three times, these are the results I get. The only thing that I can conclude so far is that the root is 2.something. How can I go further?
The most meaningful answer is probably 2.375 < root < 2.5, but I suppose you could also state that the root has the value 2.4 or 2.5 to 1dp.

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Updated: February 3, 2018
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