托马斯微积分课件31 Extreme Values of Functions.pptVIP

Chapter 3 Applications of Derivatives 3.3 The Shape of a Graph 3.1 Extreme Values of Functions 3.1.1 The Drilling-Dig Problem 3.1.1 The Drilling-Dig Problem 油井问题 3.1.2 Absolute (Global) Extreme Values 绝对极值（最值） 3.1.3 Local (Relative) Extreme Values 相对极值（极值） Exercises P234 16. P235 29, 34, 35. P236 44, 45. Example 1. 用输油管把离岸12英里的一座油井和沿岸往下20英里处的炼油厂连接起来(参见附图)。如果水下输油管的铺设成本为每英里50000美元，而陆地输油管的铺设成本为每英里30000美元。水下和陆地输油管怎么样组合才能使连接费用最少？ 1,200,000 dollars 1,166,190 dollars 1,081,025 dollars Our goal now is to find the minimum value of c(y). or Critical point Endpoint The least expensive connection costs 1,080,000 dollars, and we achieve it by running the line underwater to the point on shore y=11 mi from the refinery. * 目录 上页 下页 返回 结束 3.1 Extreme Values of Functions 3.2 The Mean Value Theorem and Differential Equations 3.4 Graphical Solutions of Autonomous Differential Equations 3.5 Modeling and Optimization 3.6 Linearization and Differentials 3.7 Newton’s Method 3.1.2 Absolute (Global) Extreme Values 3.1.3 Local (Relative) Extreme Values 3.1.4 Finding Extreme Values Example 1. 用输油管把离岸12英里的一座油井和沿岸往下20英里处的炼油厂连接起来(参见附图)。如果水下输油管的铺设成本为每英里50000美元，而陆地输油管的铺设成本为每英里30000美元。水下和陆地输油管怎么样组合才能使连接费用最少？ 50000美元 30000美元 1. Smallest amount of underwater pipe Dollar cost 2. All pipe under water Dollar cost 3. Something in between Dollar cost Example 2. Example 3. 定理1. 闭区间上连续的函数必定取到最大值与最小值。 Example 4. Extreme Depending on Continuity on Closed Interval Local Maximum Value Point Local Minimum Value Point is not a extreme value point How to find extreme value? All kinds of the points where the function achieves extreme values. 1. Critical point 2. Endpoint of the domain of f Example 5. Find the absolute maximum and minimum values of on the interval Solution. 1. Critical point 2. Endpoint Example 5. Find the absolute maximum and minimum values of on the inter