三次函數的根
Author: 藍邦偉  老師

三次函數根的性質

d = 1
c = -3
b = 0
a = 4
f(x) = a * x^(3) + b * x^(2) + c * x + d
M_1, M_2 = Extremum(f)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
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])
L_1: y = 0.5 * y(M_1) + 0.5 * y(Corner[3])
A, B_1, C_1 = Intersect(f, L_1)
L_2: y = y(M_1)
L_4: y = y(M_2)
L_5(x) = 0.5 * y(Corner[1] + M_2)
L_3(x) = 0.5 * y(M_1 + M_2)
n_1 = 1 (slider from 1 to 5, step 1)
B, C = Intersect(f, L_2)
D, E, F = Intersect(L_3, f)
G, H = Intersect(f, L_4)
I = Intersect(L_5, f)
text3: "f(x)=k有一" + (LaTeX[If[x(A) > 0, "正", "負"]]) + "根"
J = (-11.445574086599567, 6.97436483764863)