a

b

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判定

リセット

a

b

三次関数が図のとき、赤い部分を変更して\
増減表を完成させましょう。
\そこをクリックすると正負等が変わります。

D_1: false
text2 = If(D_1 ≟ true, "+", "-")
D_2: false
text3 = If(D_2 ≟ true, "+", "-")
D_3: false
D_4: false
D_5: false
D_6: false
text4 = If(D_3 ≟ true, "+", "-")
text5 = If(D_4 ≟ true, "\nearrow", "\searrow")
text6 = If(D_5 ≟ true, "\nearrow", "\searrow")
text7 = If(D_6 ≟ true, "\nearrow", "\searrow")
a_0 = 1.1 (slider from -5 to 5, step 0.1)
b_0 = -2.4999999999999996 (slider from -5 to 5, step 0.1)
c_0 = 0.1 (slider from -5 to 5, step 0.1)
d_0 = 0.2 (slider from -5 to 5, step 0.1)
func(x) = (a_0 * x^(3)) + (b_0 * x^(2)) + (c_0 * x) + d_0
M, N = Extremum(func)
func' = Derivative(func)
L_1 = Solve(func')
func'' = Derivative(func')
L_2 = Solve(func'')
O: (x(M), 0)
P: (x(N), 0)
m = Segment(M, O)
n = Segment(N, P)
p = Element(L_2, 1)
Q = Intersect(func, p, 1)
R: (x(Q), 0)
q = Segment(Q, R)
D_7: false
D_8: false
D_9: false
D_{10}: false
text12 = If(D_7 ≟ true, "+", "-")
text13 = If(D_8 ≟ true, "+", "-")
text14 = If(D_9 ≟ true, "\nearrow", "\searrow")
text15 = If(D_{10} ≟ true, "\nearrow", "\searrow")
text1: "\begin{tabular}{c|c|c|c|c|c}
x&\cdots&a&\cdots&b&\cdots\\\hline
f'(x)&\textcolor{red}{" + (LaTeX[text2]) + "}&0&\textcolor{red}{" + (LaTeX[text3]) + "}&0&\textcolor{red}{" + (LaTeX[text4]) + "}\\\hline
f(x)&\textcolor{red}{" + (LaTeX[text5]) + "}&極値&\textcolor{red}{" + (LaTeX[text6]) + "}&極値&\textcolor{red}{" + (LaTeX[text7]) + "}\\
\end{tabular}"
text11: "\begin{tabular}{c|c|c|c} 
x&\cdots&a&\cdots\\\hline
 f'(x)&\textcolor{red}{" + (LaTeX[text12]) + "}&0&\textcolor{red}{" + (LaTeX[text13]) + "}\\\hline
 f(x)&\textcolor{red}{" + (LaTeX[text14]) + "}&f(a)&\textcolor{red}{" + (LaTeX[text15]) + "} 
\end{tabular}"

Tool: Tool1
Input: A
Output: h, g

B: (x(A), 0)
C: (0, y(A))
g = Segment(A, C)
h = Segment(A, B)