The 5th-order polynomial
$f(x) = -5x^5 + 4x^4 - 12x^3 + 11x^2 - 2x + 1$
is known to be a unimodal function on interval $[-0.5, 0.5]$.
Find local minimum of this function for the given interval using following methods:
a) Golden Section method. (Initial interval: $[-0.5, 0.5]$)
b) Newton's method. (Initial point: 0)
Firstly, find results by hand for 3 iteration. Write a computer code to implement the methods, and apply your code to the problem for 10 iterations. Add your code and results (values for each step) into your solution files.
