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C3 Iteration question from a Solomon paper watch

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    I am stuck in the parts B D and E question is from a solomon.




    Thanks and Regards
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    for b) plug x=0.5 and x=1 into the equation. If there's a change of sign, then there is a root and hence 0.5<a<1

    d) If for example youre value for x4 = 1.234, then you'd plug in 0.5 above and 0.5 below you're answer (into the ORIGINAL equation), e.g. f(1.2335) and f(1.2345). If there's a change of sign then you're value of x is correct to 3dp.

    e) ...i'm thinking :p:
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    for D: say your x4 value was 1.351 , you'd do the following: let f(x)=y
    then f(1.3505) and f(1.3515), change of sign and curve continuous, therefore root.

    for E: you go on till whenever the numbers seem to be drastically changing i.e. from 1.3564 to 5.54 and say that it is divergent.
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    for b)

    all you have to do is differentiate y to find dy/dx and because it says stationary point, you know you have to make dy/dx=0 and you just have to rearrange to get the equation x= 1/4(1+ln(8root x)

    Step 1 : dy/dx= ½ x^ (- ½) - 4e^ (1-4x)
    Step 2: ½ x^ (- ½) - 4e^ (1-4x)=0
    Step 3 : rearrange :

    ½ x^ (- ½) = 4e^ (1-4x)
    Simplify the left hand side: 1/(2√x)=4e^ (1-4x)

    Take the 2√x to the other side to multiply: 2√x *4e^ (1-4x)
    So: 1=8√xe^ (1-4x)

    Take the e^ (1-4x) to the left to divide and simplify it :
    e^-(1-4x)=8√x

    e both sides:

    -(1-4x)=ln(8√x)
    Then just make the x on the left the subject
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    Hey guyz thanks for the replies
 
 
 
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