Question: Try to a build a simple optimizer to minimize: f(w)=a[]+a[1]w+a[2]w2++a[d]wd for the coefficients a=[0,0.5,2,,1]. - Plot the function f(w) ( 2 points) - Can you see where the minima is? (1 point) - Write a function that outputs f(w) and its gradient ( 3 points). - Run the optimizer on the function to see if it finds the minima (3 poimts). - Print the funciton value and number of iterations (3 points). - Instead of writing the function for a specific coefficient vector create a class that works for an arbitrary vector ( 3 points). You may wish to use the poly. polyval (w,a) method to evaluate the polynomial. import numpy.polynomial.polynomial as poly Question: Try to a build a simple optimizer to minimize: f(w)=a[]+a[1]w+a[2]w2++a[d]wd for the coefficients a=[0,0.5,2,,1]. - Plot the function f(w) ( 2 points) - Can you see where the minima is? (1 point) - Write a function that outputs f(w) and its gradient ( 3 points). - Run the optimizer on the function to see if it finds the minima (3 poimts). - Print the funciton value and number of iterations (3 points). - Instead of writing the function for a specific coefficient vector create a class that works for an arbitrary vector ( 3 points). You may wish to use the poly. polyval (w,a) method to evaluate the polynomial. import numpy.polynomial.polynomial as poly