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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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対象 9x^2+4y^2=1

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

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log_□

π

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∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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端点 f(x, y)=3x²y+y³−3x²−3y²+2

Solution

最小値(0, 2), 最大値(0, 0), 鞍点(1, 1), 鞍点(−1, 1)

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二次偏導関数テストの定義

(x, y)=(a, b) は f(x, y)
と以下の臨界点であると仮定する: D(x, y)=∂²f∂ x² ∂²f∂ y² −(∂²f∂ x∂ y )².ならば,
D(a, b) > 0 および ∂²f∂ x² <0 であれば,点 (a, b) は極大値。
D(a, b) > 0 および ∂²f∂ x² >0 であれば,点 (a, b) は極小値。
D(a, b)<0 であれば,点 (a, b) は鞍点。
D(a, b)=0 であれば,テストは失敗し,点 (a, b) は極大値,極小値,鞍点のいずれか,またはいずれでもない可能性がある。

臨界点を求める: (0, 2), (0, 0), (1, 1), (−1, 1)

∂²f∂ x² =6y−6

D(x, y)=(6y−6)²−36x²

各臨界点での符号を確認する

臨界点を確認する (0, 2): 最小値

臨界点を確認する (0, 0): 最大値

臨界点を確認する (1, 1): 鞍点

臨界点を確認する (−1, 1): 鞍点

最小値(0, 2), 最大値(0, 0), 鞍点(1, 1), 鞍点(−1, 1)

Solve instead

臨界点 3x²y+y³−3x²−3y²+2

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こんにちは, について質問する端点 f(x,y)=3x²y+y³−3x²−3y²+2 または以下のオプションから選択してください

関数の極値を見つける方法を説明する

それより解答臨界点 3x²y+y³−3x²−3y²+2

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