Course:MATH102/Question Challenge/2010 December 01e

Question

For this short-answer question, only the answers (placed in the boxes) will be marked.

If Newton’s Method is used to solve the equation x³ + x − 5 = 0, starting at x₀ = 1, what is x₁?

Hints

[show]Hint
Use y = x3 + x − 5

Solutions

[show]Solution
$x_{1}=x_{0}-{\frac {f(x)}{f'(x)}}$ $x_{1}=1-{\frac {(1)^{3}+(1)-5}{3(1)^{2}+1}}$ $x_{1}=1+3/4$ $x_{1}=7/4$