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Calculus

Derivatives

The derivative is one of the “big ideas” in calculus – capturing the notion of instantaneous rate of change and generalizing the idea of slope to more general curves. The lessons in this unit are intended to provide a strong foundation for student understanding of the derivative, especially in terms of graph. The use of the derivative as a tool for understanding behavior of functions and the implications of differentiability are also emphasized.

Calculus: Derivatives Activities

Title Type

Symmetric Secant

Investigate the symmetric secant line to provide an estimate for the derivative of a function at a point.

Alignments  Standards  |  Textbook  
  • 5132

Local Linearity

Visualize the idea of derivative as local slope.

Alignments  Standards  |  Textbook  
  • 5180

Derivative Function

Transition from thinking of the derivative at a point to thinking of the derivative as a function.

Alignments  Standards  |  Textbook  
  • 5965

Derivative Grapher

Visualize the relationship between the graph of a function and the graph of its derivative function.

Alignments  Standards  |  Textbook  
  • 5793

Critical Points and Local Extrema

Visualize the connections between the critical points and local extrema.

Alignments  Standards  |  Textbook  
  • 5734

First Derivative Test

Visualize the connections between the first derivative of a function, critical points, and local extrema.

Alignments  Standards  |  Textbook  
  • 5354

Continuity and Differentiability 1

Explore piecewise graphs and determine conditions for continuity and differentiability.

Alignments  Standards  |  Textbook  
  • 5189

MVT for Derivatives

The MVT relates the average rate of change of a function to an instantaneous rate of change.

Alignments  Standards  |  Textbook  
  • 5077

Second Derivative Grapher

Visualize the relationship between the graph of a function and the graph of its second derivative.

Alignments  Standards  |  Textbook  
  • 5031

Inverse Derivative

Visualize the reciprocal relationship between the derivative of a function and the derivative of its inverse.

Alignments  Standards  |  Textbook  
  • 5000

Continuity and Differentiability 2

Explore piecewise graphs and determine conditions for continuity and differentiability.

Alignments  Standards  |  Textbook  
  • 4397

Sign of the Derivative

Make a connection between the sign of the derivative and the increasing or decreasing nature of the graph.

Alignments  Standards  |  Textbook  
  • 4355

Slopes of Secant Lines

Collect data about the slope of a secant line and then predict the value of the slope of the tangent line.

Alignments  Standards  |  Textbook  
  • 4412

Tangent Line Demonstration

Make a connection between the slope of the tangent line at a point and the function that represents the slope at all tangent points to a function.

Alignments  Standards  |  Textbook  
  • 4509

Graphical Derivatives

Apply knowledge of the graphical relationship between a function and its derivative.

Alignments  Standards  |  Textbook  
  • 4440

Mean Value Theorem

Calculate slopes of secant lines, create tangent lines with the same slope, and note observations about the functions and slopes.

Alignments  Standards  |  Textbook  
  • 4390

Concavity

Examine the relationship between the first and second derivative and shape of a function.

Alignments  Standards  |  Textbook  
  • 4485
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