反曲點的定義
Author: 藍邦偉  老師

$ O $

決定%v次函數

$ 反曲點的定義 $

$ 若函數f在包含x_0\;的開區間$
$為連續，\;且若f\;在x_0改變其$
$凹向性的方向，則在f\;的圖形$
$上的點(x_0,f(x_0))\;稱為f\;的反$
$曲點.\;而我們稱f\;在x_0\;有一$
$個反曲點. $

$ 顯示反曲點 $

$ 反曲點的兩側分別為凹向上$
$與凹向下 $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
Q_2: 0.72 * Corner[1] + 0.28 * Corner[2]
O = (0, 0)
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
A_1 = (-1.3617817396257494, 0.7101908039224719)
A_2 = (1.140068255551467, 1.531408741270718)
A_3 = (5.303452216991415, 4.07145491958041)
A_4 = (7.7289098459036785, 1.798782023198054)
n = 0 (slider from 0 to 4, step 1)
k = 4 (slider from 3 to 5, step 1)
A_5 = (3.68011443386116, 1.3022316424758587)
A_6 = (9.333149537467694, 2.6581961436787767)
f_5 = Polynomial({A_1, A_2, A_3, A_4, A_5, A_6})
f_3 = Polynomial({A_1, A_2, A_3, A_4})
f_4 = Polynomial({A_1, A_2, A_3, A_4, A_5})
B_1 = TurningPoint(f_3)
C_1, C_2 = TurningPoint(f_4)
D_1, D_2, D_3 = TurningPoint(f_5)
f_{31} = Function(f_3, x(Q_2), x(B_1))
f_{32} = Function(f_3, x(B_1), x(Corner[2]))
f_{41} = Function(f_4, x(Q_2), x(C_1))
f_{42} = Function(f_4, x(C_1), x(C_2))
f_{43} = Function(f_4, x(C_2), x(Corner[2]))
f_{51} = Function(f_5, x(Q_2), x(D_1))
f_{52} = Function(f_5, x(D_1), x(D_2))
f_{53} = Function(f_5, x(D_2), x(D_3))
f_{54} = Function(f_5, x(D_3), x(Corner[2]))
text2: "$ 函數\;y=f(x)=\sum_{k=0}^{" + (LaTeX[If[k ≟ 3, "3", If[k ≟ 4, "4", "5"]]]) + "}{ a_k\;x^k} $"
A = (-7.786379742508313, 3.9396780877733693)