Derivative Examples Example 1 Suppose the Ball Rolling Down an Incline Lab resulted in a position vs. time function of. What is the velocity as a function.

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Presentation transcript:

Derivative Examples Example 1 Suppose the Ball Rolling Down an Incline Lab resulted in a position vs. time function of. What is the velocity as a function of time? Instantaneous Velocity

Derivative Examples Example 1 Suppose the Ball Rolling Down an Incline Lab resulted in a position vs. time function of. What is the velocity as a function of time?

Derivative Examples Example 1 Suppose the Ball Rolling Down an Incline Lab resulted in a position vs. time function of. What is the velocity as a function of time? Derivative – The instantaneous rate of change of one variable with respect to another. The instantaneous velocity is the derivative of the position with respect to time.

Derivative Rules 1.Constant Rule Where b, m and n are constants 2.Power Rule 3.General Power Rule4.Sum or Difference

Derivative Examples Example 1 Suppose the Ball Rolling Down an Incline Lab resulted in a position vs. time function of. What is the velocity as a function of time? General Power Rule

Derivative Examples Example 2 Calculate the instantaneous velocity at for each of the following position functions.

Derivative Examples Example 2 Calculate the instantaneous velocity at for each of the following position functions.

Derivative Examples Example 2 continued Calculate the instantaneous velocity at for each of the following position functions.

Derivative Examples Example 2 continued Calculate the instantaneous velocity at for each of the following position functions.