SOLUTION: Determine the abscissae of the maxima, minima and inflection points.
y = x^4 + 6x^3 - 5
The answer is supposed to be: Minimum at x point = -9/2, inflection points at x=0 and
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Question 557167: Determine the abscissae of the maxima, minima and inflection points.
y = x^4 + 6x^3 - 5
The answer is supposed to be: Minimum at x point = -9/2, inflection points at x=0 and x=-3
Help me please.
Found 2 solutions by Alan3354, gbnbgb:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Determine the abscissae of the maxima, minima and inflection points.
y = x^4 + 6x^3 - 5
---------------
y' = 4x^3 + 18x^2 = 0
--> min @ x = -9/2
-----------------
y'' = 12x^2 + 36x = 0
--> inflections @ x = 0, -3
------------------
The answer is supposed to be: Minimum at x point = -9/2, inflection points at x=0 and x=-3
Answer by gbnbgb(1) (Show Source): You can put this solution on YOUR website!
とても 容易だが
http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.557167.html
この 問題に 追加し 二重接線も 一本存在するので
====== 来年度以降の代数多様体受講生のために 敢えて 双対曲線を 求める発想で 解いておこう と 提案者D ======
https://www.google.co.jp/search?sourceid=navclient&aq=&oq=y%3D-5+%2B+6+x%5E3+%2B+x%5E4%2C+y%3D-86+%2B+54+(3+%2B+x)%2C+y%3D1%2F4+(-101+%2B+108+x)&hl=ja&ie=UTF-8&rlz=1T4GGNI_ja___JP491&q=y%3D-5+%2B+6+x%5E3+%2B+x%5E4%2C+y%3D-86+%2B+54+(3+%2B+x)%2C+y%3D1%2F4+(-101+%2B+108+x)&gs_l=hp....0.0.0.25198...........0.y_0OsBzLqj0
短縮URL
http://urx.nu/2G0U
http://www.wolframalpha.com/input/?i=y%3D-5+%2B+6+x%5E3+%2B+x%5E4%2C+y%3D-86+%2B+54+%283+%2B+x%29%2C+y%3D1%2F4+%28-101+%2B+108+x%29
と 「あっちゅうま に 叶う ことを 敢えて ね！」 です。
====== 来年度以降の代数多様体受講生のために 敢えて 双対曲線を 求める発想で 解いておこう と 提案者D ======
y=1/4 (-101 + 108 x) を A*x+B*y+1=0 に ヘンシン させ 獲た 双対曲線が 正鵠を射ているか 確認可!.
學生 D1 が 或る発想で 獲た と c と c^* を 描写 した（正しくは させた）；
http://www.wolframalpha.com/input/?i=6+x%5E2+-+x%5E3+%2B+y+%3D%3D+0%2C+4+x%5E3+%2B+27+y+%2B+108+x+y+-+36+x%5E2+y+-+864+y%5E2+%3D%3D+0
4 x^3 + 27 y + 108 x y - 36 x^2 y - 864 y^2 == 0 は 描写し難いが
特異点に 尖閣の尖点 が ふたつ と 二重点 が 在る筈 と 探求し始めた。
双対曲線を 求める発想は 多様に在るが
線型写像に 飽きた 受講生が 非線型写像 (x,y)---F-->((4 x^3+18 x^2)/(-4 x^4-18 x^3+y),-(1/(-4 x^4-18 x^3+y)))
に よる cの 像 F(c)を 求め 4 x^3 + 27 y + 108 x y - 36 x^2 y - 864 y^2 == 0
を 獲。 その 特異点達も 求め
もとの 易しい 曲線 c の 変曲点達における接線達 や
二重接線を求め 愉しんだ（血が逆流体験）。
■ 彼らの 為した 行間を確実に埋め ロハで 代数多様体の講義を受講した気分に浸ってください■
以上の 行間を埋める際
http://webcatplus.nii.ac.jp/webcatplus/details/book/8124586.html
の 関連する 頁達を 明記 して 下さい。
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