Golden-section search, Parabolic interpolation and Newton’s method

Golden-section search, Parabolic interpolation and Newton’s method
Employ the following methods to find the maximum of f(x) = 4x − 1.8×2 + 1.2×3 − 0.3×4
(a) Golden-section search (xl = _2, xu = 4, εs = 1%).
(b) Parabolic interpolation (x0 = 1.75, x1 = 2, x2 = 2.5, iterations = 4). Select new points sequentially as in the secant method. (c) Newton’s method (x0 = 3, εs = 1%).

Golden-section search, Parabolic interpolation and Newton’s method