## 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

1. asnaseer

dleather25: have you heard of the Newton-Raphson Method?

2. nikvist

$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

so do you just plug them in in th equation?

4. asnaseer

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

why did the 1 go up in the last one, but not any of the others?

6. asnaseer

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

oh okay, thanks

8. asnaseer

yw