P_1

P_2

P_3

P_4

P_5

f'

f

f'

g(x) = (-15 / 4096 * x^(5)) + (75 / 1024 * x^(4)) - (125 / 256 * x^(3)) + (75 / 64 * x^(2))
P1 = Point(g)
P2 = Point(g)
P3 = Point(g)
P4 = Point(g)
P5 = Point(g)
x1: x(P1)
x2: x(P2)
x3: x(P3)
x4: x(P4)
x5: x(P5)
f0(x) = If[x < x1, g(x)]
f1(x) = If[x1 ≤ x < x2, g(x)]
f2(x) = If[x2 ≤ x < x3, g(x)]
f3(x) = If[x3 ≤ x < x4, g(x)]
f4(x) = If[x4 ≤ x < x5, g(x)]
f5(x) = If[x5 ≤ x, g(x)]
g1(x) = g'(x)
gl1: x = x1
gl2: x = x2
gl3: x = x3
gl4: x = x4
gl5: x = x5
a = false