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f(x)=A_7 x⁷ + A_6 x⁶ + A_5 x⁵ + A_4 x⁴ + A_3 x³ + A_2 x² + A_1 x + A_0
f'(x)=7A_7 x⁶ + 6A_6 x⁵ + 5A_5 x⁴ + 4A_4 x³ + 3A_3 x² + 2A_2 x + A_1
f''(x)=42A_7 x⁵ + 30A_6 x⁴ + 20A_5 x³ + 12A_4 x² + 6A_3 x + 2A_2
f'''(x)=210A_7 x⁴ + 120A_6 x³ + 60A_5 x² + 24A_4 x + 6A_3
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f(0)=0
f(1)=1

f'(0)=v_0
f'(1)=v_1
f''(0)=a_0
f''(1)=a_1
f'''(0)=j_0
f'''(1)=j_1
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A_0 = 0
A_1 = v_0
A_2 = 1 / 2 a_0
A_3 = 1 / 6 j_0
A_4 = -5 a_0 + 5 / 2 a_1 - 2 / 3 j_0 - 1 / 6 j_1 - 20v_0 - 15v_1 + 35
A_5 = 10a_0 - 7a_1 + j_0 + 1 / 2 j_1 + 45v_0 + 39v_1 - 84
A_6 = -15 / 2 a_0 + 13 / 2 a_1 - 2 / 3 j_0 - 1 / 2 j_1 - 36v_0 - 34v_1 + 70
A_7 = 2a_0 - 2a_1 + 1 / 6 j_0 + 1 / 6 j_1 + 10v_0 + 10v_1 - 20

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