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ENDURING UNDERSTANDING
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. |
Blog Posts
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
Type 2 Questions: Linear Motion
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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. |
Blog Posts
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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. |
Blog Posts
Related Rates Problems 1
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. |
Blog Posts
Related Rates Problems 1
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. |
Blog Posts
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.
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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 
Blog Posts
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)
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Teaching Calculus 