'Decreasing functions' diaporamas de présentation

Applications of the First Derivative Applications of the Second Derivative Curve Sketching

4. Applications of the First Derivative Applications of the Second Derivative Curve Sketching Optimization I Optimization II. Applications of the Derivative. 4.1. Applications of the First Derivative. Increasing and Decreasing Functions.

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1.1

1.1. FUNCTIONS AND FUNCTION NOTATION. What Is a Function?. A function is a rule which takes certain numbers as inputs and assigns to each input number exactly one output number. The output is a function of the input. The inputs and outputs are also called variables.

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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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Applications of the First Derivative

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Section 2.2 More on Functions and Their Graphs

Section 2.2 More on Functions and Their Graphs . Increasing and Decreasing Functions. The open intervals describing where functions increase, decrease, or are constant, use x-coordinates and not the y-coordinates.

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SKETCHING THE GRAPH USING THE FIRST DERIVATIVE TEST

SKETCHING THE GRAPH USING THE FIRST DERIVATIVE TEST. Standard of Competence : 6. To use The concept of Function Limit and Function deferential in problem solving. Basic Competenc e : 6.4 To use The derived to find the caracteristic of functions and to solve the problems. Indicator :

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Increasing and Decreasing Functions and the First Derivative Test

Increasing and Decreasing Functions and the First Derivative Test. Determine the intervals on which a function is increasing or decreasing Apply the First Derivative Test to find relative extrema of a function. Standard 4.5a. y. Increasing. Decreasing. Constant. x.

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Economics 214

Economics 214. Lecture 6 Properties of Functions. Increasing & Decreasing Functions. Figure 2.6 Increasing Functions and Decreasing Functions. Example functions. Monotonic Functions. Monotonic if it increasing or if it is decreasing.

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Definition of Functions

Definition of Functions. The basic object of study in calculus is a function. A function is a rule or correspondence which associates to each number x in a set A a unique number f(x) in a set B .

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Increasing/Decreasing Functions

Increasing/Decreasing Functions. As x increases y decreases. As x increases y increases. This function is decreasing when x < 0. This function is increasing when x > 0. Remember: First derivative gives a formula for the

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An Intro to Polynomials

An Intro to Polynomials. Objectives: Identify, evaluate, add, and subtract polynomials Classify polynomials, and describe the shapes of their graphs. Classification of a Polynomial. n = 0. constant. 3. linear. n = 1. 5x + 4. quadratic. n = 2. 2x 2 + 3x - 2. cubic. n = 3.

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Work on questions for 1-2 minutes

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5.2 Mean Value Theorem

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Calculus I (MAT 145) Dr. Day Thur sday Jan 17,2013

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Curve Sketching: Role of first and second derivatives

Curve Sketching: Role of first and second derivatives. Increasing/decreasing functions and the sign of the derivative Concavity and the sign of the second derivative. Increasing/Decreasing functions. If f is defined on an interval then f is increasing if f(x 1 ) < f(x 2 ) whenever x 1 <x 2

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Functions and Their Rates of Change

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Miss Battaglia AP Calculus AB/BC

3.3 Increasing and Decreasing and the First Derivative Test Objective: Determine intervalues in which a function is increasing or decreasing and apply the First Derivative Test. Miss Battaglia AP Calculus AB/BC. Increasing and Decreasing Functions.

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Chapter 3: Applications of Differentiation

Chapter 3: Applications of Differentiation. L3.3 Increasing / Decreasing Functions and the First Derivative Test . Increasing and Decreasing Functions. If for every x 1 < x 2 on an interval f(x 1 ) < f(x 2 ) , then f is increasing [as x?, f ? ]

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