Limits

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Limits

• Calculus 2.1a part 1 of 2

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9/12/2012 Todays Learning Objective
Derivatives and the Tangent Line Problem

• You will
• Find the slope of the tangent line to a curve at
  a point.
• Use the limit definition to find the derivative
  of a function.
• Understand the relationship between
  differentiability and continuity.

• The Tangent Line Problem

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The Tangent Line Problem
Slope of a Secant Line
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The Tangent Line Problem
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The Tangent Line Problem
Difference Quotient
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Derivative Notation

• For a function,
• common notation for its derivative can be written
  as

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c (or x)
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Therefore, to find the slope at (0,1), use c 0
and to find the slope at (-1,2), use c -1
Be sure to refer back to the graph to verify that
your slopes are reasonable.
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Definition of a Derivative
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Definition of a Derivative
At (1,1)
At (4,2)
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109 p103 1, 5-8, 11-14, 17
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