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f(x) = a*x**3 + b*x**2 + c*x + d
f'(x) = 3*a*x**2 + 2*b*x + 1*c
...
d = 0       # from f(0)
c = 0       # from f'(0)
b = 3, a=-2 # from f(1) and f'(1)

f(x,y) = a*x**2 + b*y**2 + c*x*y + d*x + e*y + g
f(0,0) = 0
...
df/dy(0,0) = 0
df/dx(1,1) = 0
df/dy(1,1) = 0

p:0..1
H(p) = a*p**3 + b*p**2 + c*p**1 + d
...
    S(...) = Smin, 0, Smax, 0
V(p) = j*p**3 + k*p**2 + m*p**1 + n
    V(...) = Vmin, 0, Vmax, 0