割線斜率,切線斜率與一階導數
Author: 藍邦偉  老師

$ 割線斜率與切線斜率 $

Q

A

B

C

A = (-2.001491040048864, 0.29154961750404146)
B = (1.7361796043301738, 2.0587034681297753)
C = (3.5313835160769536, 1.4977022457089075)
f = Polynomial({A, B, C})
P = Point(f)
q: f'(x(P))
t = 2.538508959951136 (slider from x(A) to x(Corner[2]) - 0.5, step 0.01)
G = (7.805302212168631, -0.14922331655825077)
F = (6.334749161568283, 0.5383079798263274)
E = (5.303452216991415, 0.576504162958804)
D = (4.2148609977158324, 0.9775640858498079)
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: 0.78 * Corner[2] + 0.22 * Corner[3]
Q_3: (x(Corner[4]), y(Q_2))
poly1, b, c, d, e = Polygon(Corner[1], Corner[2], Q_2, Q_3)
Q: (t + 0.01, f(t + 0.01))
a = Line(P, Q)
text1: "$ m_{\overline{PQ}}=\frac{" + (LaTeX[y(Q)]) + "" + (LaTeX[If[y(P) < 0, "+", "-"]]) + "" + (LaTeX[abs(y(P))]) + "}{" + (LaTeX[x(Q)]) + "" + (LaTeX[If[x(P) < 0, "+", "-"]]) + "" + (LaTeX[abs(x(P))]) + "}=" + (LaTeX[Slope[a]]) + " $"
P_{PT}: "$ P" + (LaTeX[P]) + " $"
g = Segment(Q_2, Q_3)
text2: "$m=f'(" + (LaTeX[x(P)]) + ")= \lim_{ x \to " + (LaTeX[x(P)]) + " }\frac{f(x)-f(" + (LaTeX[x(P)]) + ")}{x" + (LaTeX[If[x(P) < 0, "+", "-"]]) + "" + (LaTeX[abs(x(P))]) + "}=" + (LaTeX[q]) + "$"