Calculus I

Using Newton's Method, determine the first approximation to the solution of:

e^(4x)= 10-2x
starting with x=0
what is x1= ??? P.S. ( the 1 is a subscript )

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  1. Let f(x)=e^(4x)-10+2x
    We look for the solution(s) of f(x)=0.

    Newton's method is essentially
    xn+1=xn-f(xn)/f'(xn)

    for
    f'(x)=4e^(4x)+2

    x0=0
    x1=x0-f(x0)/f'(x0)
    =0 - (1-10+0)/(4*1+2)
    =1.5

    x2=x1-f(x1)/f'(x1)
    =1.25
    x3=x2-f(x2)/f'(x2)
    =1.018
    x4=0.8036
    ...
    x10=0.54669824240377
    x11=0.54669824240377

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