四次函數的圖形
Author: 藍邦偉　老師

顯示極值點

顯示反曲點

四次函數的圖形

a_1

a_2

a_3

a_4

a=

b=

c=

d=

性質

顯示切線

顯示f'(x)

顯示f''(x)

e=

e

e = 0
a = 0
b = 0
c = 0
d = 0
f(x) = a * x^(4) + b * x^(3) + c * x^(2) + d * x + e
t = -8.545170082644624 (slider from x(Corner[1]) to x(Corner[3]), step 0.01)
A, B, H = Extremum(f)
C: (t, f(t))
L = Tangent(C, f)
m = Slope(L)
p_1(x) = f''(x)
D, G = TurningPoint(f)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
text3: "切線斜率m=f'(t)=" + (LaTeX[m]) + "" + (LaTeX[If[m > 0, ">", "<"]]) + "0," + (LaTeX[If[m > 0, "y=f(x)遞增", "y=f(x)遞減"]]) + ""
q: p_1(t)
t_a = false
t_b = false
text2: "f''(t)=" + (LaTeX[p_1(t)]) + "" + (LaTeX[If[q > 0, ">", "<"]]) + "0,y=f(x)開口凹向" + (LaTeX[If[q > 0, "上", "下"]]) + ""
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
inputBox4 = Textfield(d)
t_c = false
t_d = false
p_0(x) = f'(x)
t_e = false
text14: "" + (LaTeX[A]) + ""
text15: "$ " + (LaTeX[B]) + " $"
text16: "⇒f(" + (LaTeX[x(D)]) + ")=" + (LaTeX[y(D)]) + ""
text17: "$ " + (LaTeX[D]) + " $"
t_f = false
text13: "⇒f(" + (LaTeX[x(A)]) + ")=" + (LaTeX[y(A)]) + ""
text18: "$ ⇒f(" + (LaTeX[x(B)]) + ")=" + (LaTeX[y(B)]) + " $"
inputBox5 = Textfield(e)
text1: "f(x)=" + (LaTeX[a]) + "x⁴" + (LaTeX[If[b < 0, "-", "+"]]) + "" + (LaTeX[abs(b)]) + "x³" + (LaTeX[If[c < 0, "-", "+"]]) + "" + (LaTeX[abs(c)]) + "x²" + (LaTeX[If[d < 0, "-", "+"]]) + "" + (LaTeX[abs(d)]) + "x" + (LaTeX[If[e < 0, "-", "+"]]) + "" + (LaTeX[abs(e)]) + ""
text20: "" + G
text9: "⇒f'(x)=" + (LaTeX[4 * a]) + "x³" + (LaTeX[If[b < 0, "-", "+"]]) + "" + (LaTeX[3 * abs(b)]) + "x²" + (LaTeX[If[c < 0, "-", "+"]]) + "" + (LaTeX[2 * abs(c)]) + "x" + (LaTeX[If[d < 0, "-", "+"]]) + "" + (LaTeX[abs(d)]) + "=0"
text21: "" + H
text11: "⇒x=" + (LaTeX[x(A)]) + "," + (LaTeX[x(B)]) + "," + (LaTeX[x(H)]) + ""
text22: "⇒f(" + (x(H)) + ")=" + (y(H))
text10: "⇒f''(x)=" + (LaTeX[12 * a]) + "x²" + (LaTeX[If[b < 0, "-", "+"]]) + "" + (LaTeX[6 * abs(b)]) + "x" + (LaTeX[If[c < 0, "-", "+"]]) + "" + (LaTeX[2 * abs(c)]) + "=0"
E, F = Root(p_1)
text12: "⇒x=" + (LaTeX[x(E)]) + "," + (LaTeX[x(F)]) + ""
text23: "$ ⇒f(" + (LaTeX[x(F)]) + ")=" + (LaTeX[y(F)]) + " $"