Consider the following problem:
Maximize f(x) = x3 + 30x – x6 – 2x4 – 3x2.
(a) Apply the bisection method to (approximately) solve this problem. Use an error tolerance ϵ = 0.07 and find appropriate initial bounds by inspection.
(b) Apply Newton’s method, with ϵ = 0.001 and x1 = 1, to this problem.