Determine the minimum of the function from Prob. 13.11 with the following methods:

(a) Newton’s method (x0 = –1, εx = 1%).

(b) Newton’s method, but using a finite difference approximation for the derivative estimates.

ƒ’(x) = ƒ(xi + δxi) – ƒ(xi – δxi)/2δxi

ƒ’’(x) = ƒ(xi + δxi) – 2ƒ(xi) – ƒ(xi – δxi )/(δxi)2

Where δ = a perturbation fraction (= 0.01). Use an initial guess of x0 = -1 and iterate to εs = 1%.