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

Question

asnaseer · Answer

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

nikvist · Answer

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

anonymous · Answer

so do you just plug them in in th equation?

asnaseer · Answer

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

anonymous · Answer

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

asnaseer · Answer

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.

anonymous · Answer

oh okay, thanks

asnaseer · Answer

yw