Hello everyone,
Apply Newton's method to find a root of
f(x) = x^3 -7
in the interval (1, 2). If your initial guess is x0 = 2, then approximately
how far is x2 from the cube root of seven (the actual root of the equation)?
This is how I began the problem
Step 1: x - (x^3) -7)/ 3x^2
Step 2: x - (8-7)/ 12
Step 3: 2 - (1/12)
Step 4: 24/12 - 1/12 = 23/12
Step 5: [23/12 - (23/12)^3 - 7] / (3 (23/12)^3)
After step 5 I think I am close to solving it or I am doing this wrong. I have tried to get the answer but I havent come close.
Apply Newton's method to find a root of
f(x) = x^3 -7
in the interval (1, 2). If your initial guess is x0 = 2, then approximately
how far is x2 from the cube root of seven (the actual root of the equation)?
This is how I began the problem
Step 1: x - (x^3) -7)/ 3x^2
Step 2: x - (8-7)/ 12
Step 3: 2 - (1/12)
Step 4: 24/12 - 1/12 = 23/12
Step 5: [23/12 - (23/12)^3 - 7] / (3 (23/12)^3)
After step 5 I think I am close to solving it or I am doing this wrong. I have tried to get the answer but I havent come close.