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# 2.1 - The Derivative and the Tangent Line Problem

Calculus
by

## Scott Hopkins

on 26 March 2013

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#### Transcript of 2.1 - The Derivative and the Tangent Line Problem

The Derivative and the
Tangent Line Problem
2.1
Key Vocab
Derivative
The instantaneous rate of change of one variable wrt another
Differentiation
The process of finding the derivative
Average Velocity vs. Instantaneous Velocity
What's the difference?
Average velocity is the slope of the secant line. The change in position over the change in time

Instantaneous Velocity is the slope of the tangent line. The speed at one point
The Derivative
Algebraically
Examples
The Derivative
Graphically
Differentiability and Continuity
If y = f(x) has a derivative at x = c, then f(x) is continuous at x = c.
The derivative fails to exist when:
The graph of the function has a corner.
The graph of the function has a vertical tangent.
The graph of the function has a break (discontinuity).
Where is the function not differentiable?
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.
Full transcript