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anonymous

  • 4 years ago

Find an interval of length 0.1 in [1, 2] containing a root of the equation. (Enter your answer using interval notation.) x^7 + 7x − 10 = 0

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  1. asnaseer
    • 4 years ago
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    dleather25: have you heard of the Newton-Raphson Method?

  2. nikvist
    • 4 years ago
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    \[f(x)=x^7+7x-10\quad,\quad f(1)=-2\quad,\quad f(2)=132\]\[f(1.5)=17.586\quad[1,1.5]\]\[f(1.25)=3.518\quad[1,1.25]\]\[f(1.125)=0.156\quad[1,1.125]\]\[f(1.0625)=-1.034\quad\textbf{[1.0625,1.125]}\]

  3. anonymous
    • 4 years ago
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    so do you just plug them in in th equation?

  4. asnaseer
    • 4 years ago
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    yes - nikvist just started with the two extreme ends of the interval and then kept halving the interval until the solution converged to with 0.1

  5. anonymous
    • 4 years ago
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    why did the 1 go up in the last one, but not any of the others?

  6. asnaseer
    • 4 years ago
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    because at each step, you test the interval on the left and the one on the right to see which one gets you closer to the answer.

  7. anonymous
    • 4 years ago
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    oh okay, thanks

  8. asnaseer
    • 4 years ago
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    yw

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