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GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.

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Presentation on theme: "GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative."— Presentation transcript:

1 GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative

2 Definition:

3 Find the derivative:

4 2.Use definition of derivative to find the slope, rate of change, and velocity: Using the last equation for the derivative, find the slope of the tangent at x=2 Rate of change at x= -3 Instantaneous velocity at x= 9

5 Find the derivative by using the definition of derivative:

6 Find the derivative by rationalization:

7 Find the derivative by finding left and right limits

8 Differentiability Definition Theorem If f(x) is differentiable at x=a, then f(x) is continuous at x=a.

9 Different notations referring to the derivative of f(x) with respect to x

10 6. Determine the graph of the derivative

11 Tangent Line and Normal Line

12 Find the tangent line and normal line at x= -1

13 Homework 3.1 InterActMath.com

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