Consider the following function: f (x) = 1.5x6 2x4 + 12x

a) Apply three iterations of the Golden Section search to estimate the value of x that maximizes f(x). Use the initial guesses xl = 0, xu=2.

b) Apply three iterations of the parabolic interpolation method to estimate the value of x that maximizes f(x) (use Example 13.2 of the Textbook as an example). Use the initial guesses x0 =0,x1 =1andx2 =2.

c) Apply three iterations of Newtons method to estimate the value of x that maximizes f(x). Employ an initial guess of x0 = 2.

Consider the following function: f(x )