λ„ν•¨μˆ˜μ˜ ν™œμš© II (2) - ν•¨μˆ˜μ˜ κ·Έλž˜ν”„μ™€ ν•¨μˆ˜μ˜ μ΅œλŒ€·μ΅œμ†Œ

λ³Έ ν¬μŠ€νŒ…μ€ μŽˆλ‹·μ»΄ κΉ€μž¬μ€ μ„ μƒλ‹˜μ˜ μˆ˜ν•™II κ°•μ’Œλ₯Ό λ°”νƒ•μœΌλ‘œ μž‘μ„±ν–ˆμŒμ„ λ°νž™λ‹ˆλ‹€.

λ„ν•¨μˆ˜μ˜ ν™œμš© II (1) 편

 

λ„ν•¨μˆ˜μ˜ ν™œμš© II (1) - ν•¨μˆ˜μ˜ 증가와 κ°μ†Œ, ν•¨μˆ˜μ˜ κ·ΉλŒ€μ™€ κ·Ήμ†Œ, κ·Ήκ°’

ν•¨μˆ˜μ˜ 증가와 κ°μ†Œ ν•¨μˆ˜ f(x)κ°€ μ–΄λ–€ ꡬ간에 μ†ν•˜λŠ” μž„μ˜μ˜ 두 수 $x_1, x_2$에 λŒ€ν•˜μ—¬ $x_1 1️⃣ $f(x_1) 2️⃣ $f(x_1)>f(x_2)$이면 f(x)λŠ” 이 κ΅¬κ°„μ—μ„œ κ°μ†Œ ν•¨μˆ˜μ˜ 증가와 κ°μ†Œμ˜ νŒμ • ν•¨μˆ˜ f(x)κ°€ μ–΄λ–€..

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ν•¨μˆ˜μ˜ κ·Έλž˜ν”„μ™€ ν•¨μˆ˜μ˜ μ΅œλŒ€·μ΅œμ†Œ

: 1κ°œμ”©λ§Œ 쑴재! (κ·ΉλŒ€, κ·Ήμ†Œμ™€ ν—·κ°ˆλ¦¬λ©΄ μ•ˆλ¨!)

 

f(x)κ°€ [a, b]μ—μ„œ 연속일 λ•Œ μ΅œλŒ“κ°’, μ΅œμ†Ÿκ°’ κ΅¬ν•˜κΈ°

1️⃣ f'(x)둜 κ·Έλž˜ν”„μ˜ κ°œν˜• κ΅¬ν•˜κΈ°

* κ·Έλž˜ν”„ κ°œν˜• 그리기:

λ„ν•¨μˆ˜μ˜ ν™œμš© II (1) - ν•¨μˆ˜μ˜ 증가와 κ°μ†Œ, ν•¨μˆ˜μ˜ κ·ΉλŒ€μ™€ κ·Ήμ†Œ, κ·Ήκ°’ μ°Έκ³ 

 

2️⃣ κ·ΉλŒ“κ°’, κ·Ήμ†Ÿκ°’, 경계값 κ΅¬ν•˜κΈ°

* 경계값: f(a), f(b)

 

3️⃣ 2οΈβƒ£μ˜ κ°’ 쀑 κ°€μž₯ 큰 것이 μ΅œλŒ“κ°’, κ°€μž₯ μž‘μ€ 것이 μ΅œμ†Ÿκ°’!

 

 

ν•¨μˆ˜μ˜ μ΅œλŒ€·μ΅œμ†Œμ˜ ν™œμš©

1️⃣ μ λ‹Ήν•œ λ³€μˆ˜λ₯Ό x둜 놓기

2️⃣ κ΅¬ν•˜λŠ” 값을 x에 λŒ€ν•œ ν•¨μˆ˜(3μ°¨ μ΄μƒμ˜ λ‹€ν•­ν•¨μˆ˜ λ˜λŠ” 루트 μ•ˆμ˜ ν•¨μˆ˜λ‘œ λ‚˜νƒ€λ‚˜λŠ” κ²½μš°κ°€ λŒ€λΆ€λΆ„)둜 λ‚˜νƒ€λ‚΄κΈ°

3️⃣ λ―ΈλΆ„ν•˜μ—¬ 극값을 κ΅¬ν•˜κΈ°

4️⃣ x κ°’μ˜ λ²”μœ„ μ‹ κ²½μ“°λ©΄μ„œ μ΅œλŒ“κ°’/μ΅œμ†Ÿκ°’ κ΅¬ν•˜κΈ° (but.. 99.9% κ·ΉλŒ“κ°’ or κ·Ήμ†Ÿκ°’μ—μ„œ λ‚˜μ˜΄)

 


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