'Extreme value theorem' presentation slideshows

Chapter 4

Chapter 4. Applications of Derivatives. 4.1 Extreme Values of Functions. (0, 2). The Extreme Value Theorem . Local Extreme Values. Find the extreme values of . Find the extreme values of . p.193 (1-29, 35-41)odd. 4.2 Mean Value Theorem. Rolle's Theorem

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The Modeling of Rare Events: f rom Methodology to Practice a nd Back

The Modeling of Rare Events: f rom Methodology to Practice a nd Back. Paul Embrechts Department of Mathematics Director of RiskLab , ETH Zurich Senior SFI Chair www.math.ethz.ch/~embrechts. Summary:. A bit of history A bit of theory An application Further work.

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Maximum and Minimum Values ( Section 3.1)

Maximum and Minimum Values ( Section 3.1) . Alex Karassev. Absolute maximum values. A function f has an absolute maximum value on a set S at a point c in S if f(c) ? f(x) for all x in S. y. y = f(x). f(c). x. S. c. Absolute minimum values.

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AP Calculus Section 3.1 Extrema on an Interval

AP Calculus Section 3.1 Extrema on an Interval. Definitions, Theorems, and Examples. Definition. Let f be defined on an interval I containing c. 1.) f(c) is a minimum of f on I if f(c) ? f(x) for all x in I. 2.) f(c) is a maximum of f on I if f(c) ? f(x) for all x in I. Extrema.

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3.1 Extrema on an Interval

3.1 Extrema on an Interval. The mileage of a certain car can be approximated by:. At what speed should you drive the car to obtain the best gas mileage ?. The textbook gives the following example at the start of chapter 4:.

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MAXIMA AND MINIMA

MAXIMA AND MINIMA. OR How can I do the best (or worst) I can? One of the peculiarities of Mathematics is that it generally progresses when someone has a question Is my farm bigger than yours? g ave rise to Geometry How fast was that apple traveling? gave rise to Newtonian Physics

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Important Theorems about continuous functions

Important Theorems about continuous functions. Extreme Value Theorem Intermediate Value Theorem Some applications. Intuitive Picture. Imagine graph of f a 2-dimensional profile of a mountain range Tops of mountains correspond to relative maxima and bottoms of valleys to relative minima

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1 Extreme Values

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1.4 Analyzing Graphs of Functions

1.4 Analyzing Graphs of Functions. Testing for even and odd functions. Interval Notation . When the end points are included [ ]. When the end points are not included ( ). (4,8) Domain from (2, -3) to (5, -1) Written as [2, 5) Range [ -3, 8]

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4.1 Extreme Values of Functions

4.1 Extreme Values of Functions. Greg Kelly, Hanford High School Richland, Washington. The mileage of a certain car can be approximated by:. At what speed should you drive the car to obtain the best gas mileage?. Look at the following example :.

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Chapter 3

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Maximum and Minimum

Maximum and Minimum. Absolute Maximum or Minimum. A function f has an absolute maximum at c if f(c)?f(x) for all x in the domain. The number f(c) is called the maximum value of f

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Absolute Extrema

Absolute Extrema. Lesson 6.1. Fencing the Maximum. You have 500 feet of fencing to build a rectangular pen. What are the dimensions which give you the most area of the pen Experiment with Excel spreadsheet. Intuitive Definition.

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AVERAGING THINGS OUT

AVERAGING THINGS OUT. Suppose you have a given function and your boss (instructor, departmental director) orders you to estimate an average value of the infinitely many values ( one for every point in the interval ) of the function. How do you proceed?

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Minimum and Maximum Values

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Extrema on an Interval

Extrema on an Interval. Understand the definition of extrema of a function on an interval. Understand the definition of relative extrema of a function on an open interval. Find extrema on a closed interval. Standard 4.5a. Definition of Extrema.

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More about Extrema

More about Extrema. Relative Extrema. Relative Maximums. Relative Minimums. Also called Local Extrema Also called Saddle Points. Absolute Extrema. Absolute Maximum. Absolute Minimum. Also called global maximum and global minimum. Critical Points of f.

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