'Closed interval' diaporamas de présentation

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Chapter 5

Applications of Differentiation. Chapter 5. Extrema on An Interval. Section 5.1. Definition of Extrema. Let f be defined on an interval I containing c . f(c) is the minimum of f on I if f(c) ? f(x) for all x in I .

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3.2 Continuity

3.2 Continuity. JMerrill, 2009. Review 3.1. Direct substitution causes division by zero. Factoring is not possible, so what are you going to do?. Find:. x. x. f(x). f(x). -3. -1. 1. -1. -2.5. -1.5. -2. 2. -2.1. -1.9. -10. 10. -1.99. -2.01. 100. -100. -2.001. -1.999.

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UNIVERSAL FUNCTIONS

UNIVERSAL FUNCTIONS. A Construction Using Fourier Approximations. Presentation Overview An intuitive concept of Universal Functions Function Approximation and ? - Bans about Functions Fourier Interpolation on the Interval [0, 2?] Fourier Approximation on an interval [ a , b ]

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Limits and Continuity

Limits and Continuity. Limits. What is a Limit? A limit is the value a function approaches. What are the limits?. What are the Limits. Find the Limits Algebraically. Limits to Infinity. More Limits to Infinity. Continuity. What is Continuity?

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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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1.4 Continuity

1.4 Continuity. f is continuous at a if is defined. exists. Ex 1: Discontinuous where & why?. *see graph. 1.4 Continuity. 3 types of discontinuity : Removable Infinite Jump. Ex 2: Discontinuous where & why?. Ex 2: Discontinuous where & why?.

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Mean Value Theorem for Derivatives

Photo by Vickie Kelly, 2002. Greg Kelly, Hanford High School, Richland, Washington. 4.2. Mean Value Theorem for Derivatives. Teddy Roosevelt National Park, North Dakota. If f ( x ) is continuous over [ a , b ] and differentiable over ( a , b ), then at some point c between a and b :.

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3.1 Extrema on an Interval

3.1 Extrema on an Interval. Questions that will be answered in Chapter 3:. Does f have a maximum or a minimum value? Where is the function increasing or decreasing? Applications? Derivative will help us! . 3.1 Extrema on an Interval. 3.1 Extrema on an Interval .

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3.4: Intermediate Value Theorem

3.4: Intermediate Value Theorem. Pre Calculus II (CP) November 29, 2011. First, lets define. continuous function: unbroken curve can be drawn without taking your pencil off the paper. closed interval: includes the endpoints [a, b] root

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AP Calc AB

AP Calc AB. IVT. Introduction. What do we know GENERALLY about the solutions for the functions below? f(x)= cos x -2 g(x) = h(x) =. Because the function is continuous, it must take on every y value between and. Intermediate Value Theorem.

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Continuity & IVT

Continuity & IVT. Section 1.4. Continuity at a Point. A function f is continuous at c if the following three conditions are met. f(c) is defined exists. Continuity on an open interval.

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4.2 - The Mean Value Theorem

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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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8.2 Volume and Average Value

8.2 Volume and Average Value. DEFINITION: Let f be a continuous function over a closed interval [a, b]. Its average value , y av , over [a, b] is given by. Example: Find the average value Of f(x) = x 2 over the interval [0, 2].

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CONTINUITY

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1.1 Stuff

1.1 Stuff. A linear equation in one variable is an equation that has one unknown and the unknown is written to the first power. Linear equations in one variable can be written in the form ax + b = 0 where a and b are real numbers and . 1.4 Stuff.

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Continuity, the Intermediate Value Theorem, and the Bisection Method

Continuity, the Intermediate Value Theorem, and the Bisection Method . Continuity, IVT & Bisection Method. A function is continuous at a point c if and only if a. is defined b. exists c. the two are equal; i.e. .

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Continuity and One-Sided Limits

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