Higher Order Derivative

Higher Order Derivatives
Higher Order Derivatives are a derivative of a derivative.

Example :

The second derivative describes how the first derivative is changing.


Derivatives and Speed
If you are given an equation for speed, the derivative of that equation is velocity and the derivative of the velocity equation is acceleration.

When you have a positive velocity that goes to a more positive velocity you have an acceleration.
When you have a negative velocity that goes to a more negative velocity you have an acceleration.

If you graph the velocity equation on your calculator you can find the acceleration. As the velocity is the slope of the line tangent to the speed equation, the acceleration is the maximum or minimum of the velocity equation.

Finding the Equation when given the Derivative Values

If you are given several of the derivative values you can find the equation that started it. If they give you dervatives up to a third derivative then you know the equation is a third degree polynomial, and so on.

EXAMPLE PROBLEM
Find the equation if you are given these derivatives.

1. You are given the values of the derivatives.



2. Depending on the degree you right the several polynomials with a, b, and c.


3. You start with the last equation and you make it equal to the last derivative value.


4. Just work your way up! (plug in answers of previous derivatives)

5. The equation will be equal to this : (ANSWER)

LINKS:

http://tutorial.math.lamar.edu/AllBrowsers/2413/HigherOrderDerivatives.asp

http://www.pinkmonkey.com/studyguides/subjects/calc/chap4/c0404f01.asp

PERSONALIZATION:

my favorite inspiration quote.

good better best, never let it rest, until the good is better, and the better is the best.

KYONG YOUR UP NEXT!!!! :)