Question

Let f be twice continuously differentiable function on the interval $[ a,b ]$ with $p \epsilon[ a,b ]$and f(p) = 0. Further, suppose that $f^{'} (p)\neq 0$ . Show thatthere exists $\delta \ \textgreater \ 0$ such that for $p_{0} \epsilon I =[ p- \delta ,p+ \delta ]$, the sequence {pn}generated by Newton’s method converges to p.

Answer 1

u do itself try it or ask to ur teacher