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. 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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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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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. 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. 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. 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. 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. 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. 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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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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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. 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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