Tangent Line EXDetermine the slope of the line

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Tangent Line範例 EX：Determine the slope of the line tangent to the graph of Sol：

Tangent Line範例 EX：Determine the slope of the line tangent to the graph of Sol： -2 -1 1 2 3 ∴當 at point (-2, 4) is 2(-2)= -4 7

3 -1 前言 • When the derivative exists, the function is said to be

3 -1 前言 • When the derivative exists, the function is said to be differential • To differentiate a function means to determine its derivative • 有關微分的寫法及念法如下 , , , 葉布尼茲的寫法 9

Derivative練習 1. EX： If then ( ) Sol： ( ) 12

Derivative練習 1. EX： If then ( ) Sol： ( ) 12

3 -2 Basic Rule for Differentiation 1. 1. 1 c c：constant 2. 2. 1

3 -2 Basic Rule for Differentiation 1. 1. 1 c c：constant 2. 2. 1 3. 4. 13

Basic Rule for Differentiation範例 , 1. 1 若 , 1. 2 若 , 2.

Basic Rule for Differentiation範例 , 1. 1 若 , 1. 2 若 , 2. 1 若 , 2. 2 若 2. 3 若 , , 14

Marginal Analysis範例 1. EX： Suppose ( )determine the marginal cost when Sol： (即生產到第 9個，其邊際成本約為

Marginal Analysis範例 1. EX： Suppose ( )determine the marginal cost when Sol： (即生產到第 9個，其邊際成本約為 12元) (生產到第 10個，其邊際成本約為 10元) ︰ ︰ 25

Marginal Analysis範例 1. EX： Suppose . The company determine to stop producing table when

Marginal Analysis範例 1. EX： Suppose . The company determine to stop producing table when the marginal cost reaches $100. How many table will be mode? Sol： (邊際成本) 已知 ∴這個公司會生產到 1500個桌子後停止生產 26

3 -4 Marginal Analysis (邊際分析) 2. 除了Marginal cost，其他類似的邊際分析亦可同 理來解它，例如Marginal revenue 或Marginal profit (回顧第一章已知 )

3 -4 Marginal Analysis (邊際分析) 2. 除了Marginal cost，其他類似的邊際分析亦可同 理來解它，例如Marginal revenue 或Marginal profit (回顧第一章已知 ) 27

Marginal Analysis範例 , EX：若 ① 求marginal cost (MC)，marginal revenue (MR) ② 求MR(5) ③ 求marginal

Marginal Analysis範例 , EX：若 ① 求marginal cost (MC)，marginal revenue (MR) ② 求MR(5) ③ 求marginal profit (MP) ④ 求 , 當MC=MR Sol： ① ② ③ ④ MC RC 28

3 -5 The Product (積) & Quotient Rule (商) 3. Product Rule： , 或

3 -5 The Product (積) & Quotient Rule (商) 3. Product Rule： , 或 即 30

Product Rule範例 EX： , 求 Sol： 32

Product Rule範例 EX： , 求 Sol： 32

3 -5 The Product (積) & Quotient Rule (商) 4. Quotient Rule 34

3 -5 The Product (積) & Quotient Rule (商) 4. Quotient Rule 34

Quotient Rule範例 EX： , find the derivative of Sol： EX： , find Sol： 35

Quotient Rule範例 EX： , find the derivative of Sol： EX： , find Sol： 35

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