Answer to Question #305611 in Differential Geometry | Topology for Junior

Question #305611

use the Bisection method with 3 iterations to find solutions for f(x) = x ^ 3 + x - 4 on interval [1, 4] .

1
Expert's answer
2022-03-07T08:05:02-0500

"f(x)=x^3+x-4\\\\\n\\left[1,4\\right]\\\\\na=1, b=4,a<b\\\\\nf(a)=f(1)=1+1-4=-2\\\\\nf(b)=f(4)=4^3+4-4=64\\\\\nf(a)f(b)=-2\\cdot64<0\\\\\nx_0=\\frac{a+b}{2}=\\frac{1+4}{2}=2.5\\\\\nf(x_0)=f(2.5)=2.5^3+2.5-4=14.125\\\\\nf(a)f(x_0)=-2\\cdot14.125<0, b=x_0=2.5\\\\\nx_1=\\frac{1+2.5}{2}=1.75\\\\\nf(x_1)=f(1.75)=1.75^3+1.75-4=3.109\\\\\nf(a)f(x_1)=-2\\cdot3.109<0, b=1.75\\\\\nx_2=\\frac{1+1.75}{2}=1.375\\\\\nf(x_2)=1.375^3+1.375-4=-0.025\\\\\nx=1.375"


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