Chapter 22.1, Problem 10P

CAS EXPERIMENT. Steepest Descent. (a) Write a program for the method.
(b) Apply your program to $f\left(x\right)=x_1^2+4x_2^2$ , experimenting with respect to speed of convergence depending on the choice of $x_0$ .
c) Apply your program to $f\left(x\right)=x_1^2+x_2^4$ and to $f\left(x\right)=x_1^4+x_2^4,x_0=\left(2,1\right)$ . Graph level curves and your path of descent. (Try to include graphing directly in your program.)