Unit 4 Contextual Applicationsap Calculus
Contextual questions requiring students to compute and interpret a derivative using correct units, especially if the given function is already a rate. Approximation of function values using linearization and tangent line applications. Interpretation of an approximation as an underestimate or an overestimate. Unit 4 - Contextual Applications of Differentiation Local Linearity and Linearization. This helps us a function using the tangent line to the curve. If f(a) = a number you know and x is very close to a, then you do approximate f(x) by: f(x) = EX#1 - What is the approximate value of f(x) = 3 x when x = 8.2?
- Unit 4 Contextual Applicationsap Calculus Answers
- Unit 4 Contextual Applicationsap Calculus Pdf
- Unit 4 Contextual Applicationsap Calculus 1
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ENDURING UNDERSTANDING
Unit 4 Contextual Applicationsap Calculus Answers
CHA-3 Derivatives allow us to solve real-world problems involving rates of change.
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Topic Name | Essential Knowledge |
4.1 Interpreting the Meaning of the Derivative in Context LEARNING OBJECTIVE CHA-3.A Interpret the meaning of a derivative in context. | CHA-3.A.1 The derivative of a function can be interpreted as the instantaneous rate of change with respect to its independent variable. |
CHA-3.A.2 The derivative can be used to express information about rates of change in applied contexts. | |
CHA-3.A.3 The unit for is the unit for f divided by the unit for x. |
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At Just the Right Time A good problem
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4.2 Straight Line Motion: Connecting Position, Velocity, and Acceleration LEARNING OBJECTIVE CHA-3.B Calculate rates of change in applied contexts. | CHA-3.B.1 The derivative can be used to solve rectilinear motion problems involving position, speed, velocity, and acceleration. |
Blog Posts
The Ubiquitous Particle Motion Problem – a PowerPoint Presentation and its Handout
Motion Problems: Same Thing Different Context (11-16-2012) Matching Motion (9-16-2016)
Motion Matching A quick quiz
Speed (11-19-2012)
Speed Activity An exploration on Speed
A Note on Speed (4-21-2018) An analytic approach
Brian Leonard’s Particle Motion Game Velocity Game and answers Velocity game Answers
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4.3 Rates of Change in Applied Contexts Other than Motion LEARNING OBJECTIVE CHA-3.C Interpret rates of change in applied contexts. | CHA-3.C.1 The derivative can be used to solve problems involving rates of change in applied contexts. |
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4.4 Introduction to Related Rates LEARNING OBJECTIVE CHA-3.D Calculate related rates in applied contexts. | CHA-3.D.1 The chain rule is the basis for differentiating variables in a related rates problem with respect to the same independent variable. |
CHA-3.D.2 Other differentiation rules, such as the product rule and the quotient rule, may also be necessary to differentiate all variables with respect to the same independent variable. |
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Related Rates Problems 1
Related Rate Problems II
Good Question 9 Baseball and Related Rates
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4.5 Solving Related Rate Problems LEARNING OBJECTIVE CHA-3.E Interpret related rates in applied contexts. | CHA-3.E.1 The derivative can be used to solve related rates problems; that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known. |
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Related Rates Problems 1
Related Rate Problems II
Good Question 9 Baseball and Related Rates
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4.6 Approximating Values of a Function Using Local Linearity and Linearization LEARNING OBJECTIVE CHA-3.F Approximate a value on a curve using the equation of a tangent line. | CHA-3.F.1 The tangent line is the graph of a locally linear approximation of the function near the point of tangency. |
CHA-3.F.2 For a tangent line approximation, the function’s behavior near the point of tangency may determine whether a tangent line value is an underestimate or an overestimate of the corresponding function value. |
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Local Linearity The graphical manifestation of the derivative
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ENDURING UNDERSTANDING
LIM-4 L’Hospital’s Rule allows us to determine the limits of some indeterminate forms.
Unit 4 Contextual Applicationsap Calculus Pdf
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4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms LEARNING OBJECTIVE LIM-4.A Determine limits of functions that result in indeterminate forms. | LIM-4.A.1 When the ratio of two functions tends to or in the limit, such forms are said to be indeterminate. |
LIM-4.A.2 Limits of the indeterminate forms or may be evaluated using L’Hospital’s Rule. |
EXCLUSION STATEMENT: There are many other indeterminate forms, such as , for example, but these will not be assessed on either the AP Calculus AB or BC Exam. However, teachers may include these topics, if time permits.
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Determining the Indeterminate 1
Determining the Indeterminate 2 Same name, different post. Examining an implicit relation
Locally Linear L’Hôpital Demonstrating L’Hôpital’s Rule (a/k/a L’Hospital’s Rule)
Unit 4 Contextual Applicationsap Calculus 1
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