#### 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.

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