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Math Help - use Newton's method to solve the problem

  1. #1
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    Question use Newton's method to solve the problem

    use Newton's method to find a solution for each equation in the given intervals. Find all solution to the nearest hundredth.

    A) 3x^4 + 4x^3 -6x^2 -2x -12 =0 [-3,-2] ,[1,2]

    This one have two interval , so how can I do ? it's that I have to pick up two numbers for each interval and solved it?

    B) e^2x + 3x -4 =0 [0,3]

    I really sick on the exponential function.......help me!~~


    thanks!~
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  2. #2
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    Quote Originally Posted by shannon1111 View Post
    use Newton's method to find a solution for each equation in the given intervals. Find all solution to the nearest hundredth.

    A) 3x^4 + 4x^3 -6x^2 -2x -12 =0 [-3,-2] ,[1,2]

    This one have two interval , so how can I do ? it's that I have to pick up two numbers for each interval and solved it?

    B) e^2x + 3x -4 =0 [0,3]

    I really sick on the exponential function.......help me!~~


    thanks!~
    The first equation is a quartic, and it has 4 roots. Newton's method only returns 1 root though, and you are asked to find 2. But you are given the interval of two of the roots, so if you pick a starting value in each of those intervals, it is likely to converge to the root in that interval, and not another root. So do the process twice for that questions, the first time use a starting value from the first interval, and the 2nd time use a starting value from the 2nd interval and you should get two different answers which are both correct.

    For the exponential:

     f(x) = e^{2x}+3x-4

     f'(x) = 2e^{2x} + 3

    Just use a calculator when inputting the numbers...
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