' - - File: III_Zero1b.txt
'     REFER TO PART II: ADVANCED GRAPHS, IV--THE DERIVATIVE TO RECEIVE
'     AN ADVANCE READ OF THE DERIVATIVE, IF NECESSARY.

' Continue analysis from file, IIIZero1. Use the derivative to find the zeros for the location
'    of the minimum and maximum of Fc{t}. 

to = 0.00001
Fc{t} = t^2 - 2^t   :  Hc<t> = <t, Fc, 0>
Fd{t} = Diff[Fc,t]  :  Hd<t> = <t, Fd, 0>    
'         Do a quick plot of Fd to locate the zeros estimates.
'         (Comment out the statements below the dash line and do the plot:
Plot[Hd, {t, -3,5,100}]   ' Increase plot range as need by observaton of plot.
'        By inspection, the two ranges are (0,1) & (3,3.5).
'        Insert Fd & ranges into the Zero[ statements and remove the remark symbol.
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Zero[Fd, {0,1,z1} to]              ' Note syntax. z1 (left undefined) will store the results.
'@Zero = @z1!

Zero[Fd,{3,3.5, z2} to]       
'@Zero = @z2!

<t = 1>                                      ' IMPORTANT: any value required to display the zeroes.

' Note the new means to  display the results. Check file Zero1.txt or III_Start2.txt!

