Answer to Question #305568 in Differential Equations for Junior

Question

Use the Bisection method with 3 iterations to find solutions for f(x) = x3 + x - 4 on interval [1; 4].

Answer 1

f(1)=1+1-4=-2

f(4)=64+4-4=64

Iteration 1

M=(1+4)/2=2.5

f(2.5)=15.625+2.5-4=14.125

As f(M)>0

[1,2.5]

Iteration 2

M=(1+2.5)/2=1.75

f(1.75)=5.359375+1.75-4=3.109375

As f(M)>0

[1, 1.75]

Iteration 3

M=(1+1.75)/2=1.375

f(1.375)=-0.02539062

As f(M)<0

x=1.375