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Definition of the Derivative

Author:
Kristen Beck
Topic:
Calculus, Derivative
Select the limit that you would like to evaluate, and then move the slider to change the value of . Notice that:
  • the difference quotient (in blue) is equal to the slope of the secant line to passing through and , and
  • the limit of the difference quotients (in red) is equal to the slope of the tangent line to at .
Why is it clear that is differentiable at ?

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