Definition of the derivative

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After completing this section, students should be able to do the following.

Use limits to find the slope of the tangent line at a point.
Understand the definition of the derivative at a point.
Compute the derivative of a function at a point.
Estimate the slope of the tangent line graphically.
Write the equation of the tangent line to a graph at a given point.
Recognize and distinguish between secant and tangent lines.
Recognize different notation for the derivative.
Recognize the the tangent line as a local approximation for a differentiable function.