Hello,
y= x^3-4x²-3x+18=(x-3)²*(x+2)
y'=3x²-8x-3
y''=6x-8
1) Stationary points
Maximun: x=-1/3 ==>y=18,5185....
Minimum: x=3 ===>y=0 (double root)
2) x=4/3: point of inflection. (y''=0 and change sign)
Im going to guess you want a sinusoidal function. Its been a while but I can tell you most of it
(443-28)/2 is the amplitude
28 minutes is the period
40-28 is the horizontal shift
(443-28)/2+28 is the vertical shift