The Student Room Group

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(edited 6 years ago)
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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(edited 6 years ago)
ye just go with the third one then
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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