Definition of the Derivative

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# Definition of the Derivative - PowerPoint PPT Presentation

Definition of the Derivative. Derivatives Review- 1. Tangent Line Problem . The tangent line can be found by finding the slope of the secant line through the point of tangency and a point on the curve. Theorem 2-1. Differentiability implies continuity Not the other way around.

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### Definition of the Derivative

Derivatives Review- 1

Tangent Line Problem

The tangent line can be found by finding the slope of the secant line through the point of tangency and a point on the curve

Theorem 2-1

Differentiability implies continuity

Not the other way around

Definition of the Derivative

For a function f(x) the average rate of change along the function is given by:

Which is called the derivative of f

Notation:

Piecewise derivatives.

• Find f’(3)
• Find f’(4)
• Find f’(0)
Home Work

Page 104 # 5-23 odd and # 39-48