Please code the Golden section search and newton optimization to solve the exercises. Optimization of functions Find a local maximum or minimum 7.3 Locate the minimum of the function f(x)=3+6x+5x2+3x3+4x4 7.2 Determine the maximum and the corresponding value of x for the function f(x)=x2+8x12 7.4 Given f(x)=1.5x62x4+12x (a) Plot the function. (b) Use analytical methods to prove that the function is concave for all values of x. (c) Find the maximum f(x) and the corresponding value of x