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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  
  • 5161

Local Linearity

Visualize the idea of derivative as local slope.

Alignments  Standards  |  Textbook  
  • 5202

Derivative Function

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

Alignments  Standards  |  Textbook  
  • 5999

Derivative Grapher

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

Alignments  Standards  |  Textbook  
  • 5827

Critical Points and Local Extrema

Visualize the connections between the critical points and local extrema.

Alignments  Standards  |  Textbook  
  • 5757

First Derivative Test

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

Alignments  Standards  |  Textbook  
  • 5388

Continuity and Differentiability 1

Explore piecewise graphs and determine conditions for continuity and differentiability.

Alignments  Standards  |  Textbook  
  • 5213

MVT for Derivatives

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

Alignments  Standards  |  Textbook  
  • 5100

Second Derivative Grapher

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

Alignments  Standards  |  Textbook  
  • 5053

Inverse Derivative

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

Alignments  Standards  |  Textbook  
  • 5023

Continuity and Differentiability 2

Explore piecewise graphs and determine conditions for continuity and differentiability.

Alignments  Standards  |  Textbook  
  • 4416

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  
  • 4375

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  
  • 4434

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  
  • 4533

Graphical Derivatives

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

Alignments  Standards  |  Textbook  
  • 4458

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  
  • 4408

Concavity

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

Alignments  Standards  |  Textbook  
  • 4503
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