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Derivative Definition Lesson

Author:L. Marizza A. Bailey, Rick Hollenbeck

Definition of a Derivative

The derivative of at is the slope of the tangent line to at x = a, and is denoted The graph below is interactive. You can change the function, and the x-value for a, and the value of h. To understand the lesson correctly, follow these instructions.
  1. Click on "First Point". This is the point at which you want to find the derivative.
  2. Click on "Second Point". This is a variable point that will help you find the derivative
  3. Click on "Secant Line". This is the line through and . Write the slope formula for the secant line on a piece of paper (because you will need it later)
  4. Move "h" so that it "approaches 0". Write the limit expression involving what you wrote in part 3 and "h approaching 0"
  5. Move "a" around and take note of the behavior of the slope of the tangent line. Where is it positive? Where is it negative? Where is it 0?
  6. Now change the function to and repeat #5.
  7. Change the function to and repear #5.

Slope of Secant and Tangent Line

The parabola

Using the graph of , which of the following statements are true about

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  • A
  • B
  • C
  • D
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The parabola

Using the graph of , which of the following statements are true about

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  • A
  • B
  • C
  • D
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The parabola

Using the graph of , which of the following statements are true about

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  • A
  • B
  • C
  • D
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The cubic

Using the graph of , which of the following statements are true about

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  • B
  • C
  • D
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The cubic

Using the graph of , which of the following statements are true about

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  • B
  • C
  • D
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The cubic

Using the graph of , which of the following statements are true about

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  • A
  • B
  • C
  • D
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The sine graph

Using the graph of , which of the following statements are true about

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  • A
  • B
  • C
  • D
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The Exponential Graph

Using the graph of , which of the following statements are true about

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  • B
  • C
  • D
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The Log Graph

Using the graph of , which of the following statements are true about

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  • A
  • B
  • C
  • D
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The Absolute Value Graph

Using the graph of , which of the following statements are true about

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  • A
  • B
  • C
  • D
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Fill in the blank

When the graph of is increasing, then is

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  • B
  • C
  • D
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Fill in the blank

When the graph of is decreasing, then is

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  • A
  • B
  • C
  • D
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Fill in the blank

When the graph of has a corner, then is

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  • A
  • B
  • C
  • D
Check my answer (3)

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