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    the normally the q will specify either the number of times you have to do it or the accuracythe answer has to be to
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    ye just go with the third one then
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    (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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