Warm Up

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# Warm Up - PowerPoint PPT Presentation

Warm Up. Find the slope of the tangent line to at x=2. Answer: m= -4. Derivative of a Function. 3.1. Goal. I will be able understand the relationship between a function and its derivative as well as recognize when a function will not be differentiable. New calendar . Definition.

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Presentation Transcript
Warm Up
• Find the slope of the tangent line to

at x=2.

### Derivative of a Function

3.1

Goal
• I will be able understand the relationship between a function and its derivative as well as recognize when a function will not be differentiable.
• New calendar
Definition
• The derivative is the formula for slope of a tangent line, instantaneous speed, or velocity of an object.
Alternate Formula
• If asked to find the derivative at a point x=a.
Notation
• There are many ways to denote the derivative. They can all be found at the top of page 101.
• I will also give them to you now…

“the derivative of f with respect to x”

Y prime

“the derivative of y with respect to x”

“the derivative of f with respect to x”

“the derivative of f of x”

Note:

dx does not mean d times x !

dy does not mean d times y !

does not mean !

does not mean !

Note:

(except when it is convenient to think of it as division.)

(except when it is convenient to think of it as division.)

Example
• Use the definition to find the derivative of at a=1.