Consider minimizing the one-dimensional function
by Newton's
method. You might want to transform this problem into a root-finding
one: 
. Newton's method was originally devised for solving
nonlinear equations and then extended for minimization. Roughly
speaking, the Newton techniques we learned above for minimizing 
can
be adapted to solve nonlinear equations of form 
.
While good graphics skills can be very effective for minimizing or finding the roots of one-dimensional problems, we cannot expect to solve such problems systematically when many variables are involved and for repeated applications. The following exercises will give you practical experience in solving such problems using graphics and suitable programs.
