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    We need to find using Newtons method the root to  f(x)= x^3-4x^2+4x .

    Now this is undefined if  x=2 \rightarrow f'(x)=0 .Our lecturer says let  x_0=1 . Now we get the iteration

     x_{n+1}=2(x_{n})^2/(3x_{n}-2) Iff for any n, x_n is not equal to 2. However  x_{2}=2 . He then want's us to say whether the sequence is monotonic and whether or not it's increasing. However this sequence doesn't even exist for  x_{0}=1 . Do you think he's made a msitake?
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    (Original post by psanghaLFC)
    We need to find using Newtons method the root to  f(x)= x^3-4x^2+4x .

    Now this is undefined if  x=2 \rightarrow f'(x)=0 .Our lecturer says let  x_0=1 . Now we get the iteration

     x_{n+1}=2(x_{n})^2/(3x_{n}-2) Iff for any n, x_n is not equal to 2. However  x_{2}=2 . He then want's us to say whether the sequence is monotonic and whether or not it's increasing. However this sequence doesn't even exist for  x_{0}=1 . Do you think he's made a msitake?
    well think about what newstons method does? and what does a monotonic graph mean?

    and from what you have said - how can this help you come to a conclusion?
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    (Original post by psanghaLFC)
    We need to find using Newtons method the root to  f(x)= x^3-4x^2+4x .

    Now this is undefined if  x=2 \rightarrow f'(x)=0 .Our lecturer says let  x_0=1 . Now we get the iteration

     x_{n+1}=2(x_{n})^2/(3x_{n}-2) Iff for any n, x_n is not equal to 2. However  x_{2}=2 . He then want's us to say whether the sequence is monotonic and whether or not it's increasing. However this sequence doesn't even exist for  x_{0}=1 . Do you think he's made a msitake?
    oh also it is undefined when x = 2, x_2 = 2 is another matter =P
 
 
 
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