use newtons method to solve

Question

Starting with x₁= 2, use Newton's method to solve (to 4 decimal places):

Answer 1

f(x) = x³-2x-5

f'(x)=3x²-2

x₂=x₁- [f(x₁)/f'(x₁)]

x₂=2-[-1/10]=2.1

x₃=x₂-[f(x₂)/f'(x₂)]

x₃=2.1-[.061/11.23] =2.0945... ...

And so on...

Here is a Desmos graph that takes it to x₆ (starting with x₀=2)

desmos.com/calculator/oamokwopmy