The Language of Functions and Continuity · Algebraic Thinking

Rate of Change and Tangency

Transitioning from average rate of change to the concept of the derivative at a point.

Key Questions

  1. 1How can a secant line be transformed into a tangent line through the use of limits?
  2. 2Why does the slope of a curve at a single point provide more information than a linear average?
  3. 3What does the existence of a derivative tell us about the smoothness of a function?

Common Core State Standards

CCSS.Math.Content.HSF.IF.B.6CCSS.Math.Content.HSF.LE.A.1
Grade: 12th Grade
Subject: Mathematics
Unit: The Language of Functions and Continuity
Period: Algebraic Thinking

Suggested Methodologies

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