(* finding local minima for a function of one variable *) 
(* To run on command line:  math -run "<<hw4.min.math" *)
(* The above line assumes that math kernel is aliased to "math" *)
(* For example, on my machine alias math='/Applications/Mathematica.app/Contents/MacOS/MathKernel' *) 
(* or simply use << fmin1D.math once math kernel is already running *) 

<<JavaGraphics`

<<Optimization`UnconstrainedProblems`


(* a nice function, well-behaved on [1, 1] *) 

   F[x_] := 0.01x^2 + x^4;  
  


x0 = 0.1 (* A reasonable starting Point *)


(* Newton's with automatic parameter selection *) 

 answer = FindMinimum [F[x], {x}, Method -> Newton ]   

FindMinimumPlot [F[x], {{x, x0}}, Method -> Newton, PlotStyle->{Thick}, BaseStyle->{FontWeight->"Bold", FontSize-> 16}  ]

xmin =  x /. answer[ [2] ] 
ymin = answer[ [1] ]

Print["  "]
Print["Value of X that minimizes F, xmin =   ", xmin]
Print["  "]
Print["                          F(xmin)=     ", ymin]
Print[" "]