導函數
Author: 藍邦偉  老師

$ 導函數 $

Q

A

B

C

$ f'(x)=\lim_{ h \to 0 }\frac{f(x+h)-f(x)}{h} ,f'(a)=\lim_{ h \to 0 }\frac{f(a+h)-f(a)}{h}$

t = 0.9710120160033073 (slider from x(Corner[1]) + 0.5 to x(Corner[2]) - 0.5, step 0.01)
C = (3.5313835160769536, 1.4977022457089075)
B = (1.7361796043301738, 2.0587034681297753)
A = (0.6001521289279139, 1.5117272762694292)
f = Polynomial({A, B, C})
P: (t, f(t))
q: f'(x(P))
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)
P_{PT}: "$ P" + (LaTeX[P]) + " $"
g = Segment(Q_2, Q_3)
list_1 = Sequence(x(P) + 0.01 * k, k, -5, 5)
list_2 = Sequence(f(x(P) + 0.01 * k), k, -5, 5)
list_3 = Sequence(f'(x(P) + 0.01 * k), k, -5, 5)
h = Tangent(P, f)
k = 8 (slider from 1 to 11, step 1)
text1: "       $ a=" + (LaTeX[Element[list_1, k]]) + " ⇔x$
  $f(a)=" + (LaTeX[Element[list_2, k]]) + "⇔f(x)$
$f'(a)=" + (LaTeX[Element[list_3, k]]) + "⇔f'(x)$"