Here's a proof question please answer clearly, as it will be rated accordingly!

Problem 2 [3 pts]: Find an example to show that Newton's method when it converges does not necessarily do so at quadratic rate, even if the function is infinitely differentiable. In other words, find an infinitely differentiable function f(x) and an initial guess xo, for which Newton's method converges at a rate that is clearly lower than the quadratic rate (e.g., linearly). Show the rate of convergence analytically or numerically. Problem 2 [3 pts]: Find an example to show that Newton's method when it converges does not necessarily do so at quadratic rate, even if the function is infinitely differentiable. In other words, find an infinitely differentiable function f(x) and an initial guess xo, for which Newton's method converges at a rate that is clearly lower than the quadratic rate (e.g., linearly). Show the rate of convergence analytically or numerically