Derivatives by Definition

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Presentation transcript:

Derivatives by Definition The Long Way (no shortcuts!!)

Definition The derivative is the slope of a curve at a point. Notation: y’ = f’(x)=

The Theory If Q slides really close to P, then the slope of the secant line becomes very very close to the slope of the tangent line. What do I mean?? P Q Q Q P P

What is the formula? Since it’s a slope equation, its based on If we take the limit as h gets very very small (h being the x distance between P and Q) we get

The Definition of a Derivative

Examples