' - - File: XI_Family3.txt

' The set of curves below taken from VITan1 shows a tangent line.

a=0.25                                        ' Our constant ID to vary per each frame.
x1 = 1                                          ' Point chosen for the line tangent to the curve.
                                                     ' Try x = 0.25 and y = 1 for scales.
R<t> = <t, -2*t^3 + 3*a*t, 0>
D<t> = vDiff[R]
T<t> = vDiv[D,sMag[D]]            ' dR/dt / |dR/dt|  =  Dr/ds  = T (tangent vector)
Rn<t> = vEval[R,x1]                  ' Point chosen for tangent line.
Tn<t> = vEval[T,x1]
L<t> = vAdd[vMpy[Tn,#],Rn]    ' Tangent line; recall # replaces "t" in vector math.

t0 = -2  :  tf = 2  :  n = 100
Plot[R,L, {t, t0, tf, n}]

' Adjust X-scale = 0.5 and Y-scale = 2 units BEFORE starting the curves.




