Consider finding the minimum of the function
by
the structure described in algorithm 2.1.
This nonlinear function
is essentially a quadratic function perturbed by small sinusoidal
fluctuations. One can use several simple techniques as a first
approach to solving this problem. These include graphics, tabulation
of function values, and bisection to bracket the interval where a
minimum lies.
a) Plot this function.
b) Plot its derivative
; solving for the roots of 
is a closely related
problem to minimizing 
.
c) Choose various initial points
devise descent paths toward the minimum of 
.
d) Plot your paths toward the minimum and analyze the results.
