Term
What is a Derivative?
------------ |
|
Definition
Slope
------------
Instantaneous Rate of Change
------------ |
|
|
Term
What is the Derivative of this problem?
Ax^B
---------- |
|
Definition
|
|
Term
How do you find Average Rate of Change?
----------- |
|
Definition
f(x1)-f(x2)/x1-x2
------------------ |
|
|
Term
When is Slope Undefined?
------------ |
|
Definition
When a line is vertical, its slope is undefined
------------------------ |
|
|
Term
What is the Slope of a Horizontal Line?
------------ |
|
Definition
|
|
Term
Point Slope Formula
-------------- |
|
Definition
|
|
Term
How do you find the marginal version of a function?
------------------------- |
|
Definition
Take the Derivative of the function
------------ |
|
|
Term
What are the critical points of a function?
-------------- |
|
Definition
Every maximum, minimum, and where a function breaks
--------------- |
|
|
Term
What are the critical points of a function?
-------------- |
|
Definition
Every maximum, minimum, and where a function breaks
--------------- |
|
|
Term
How do you calculate slope?
------------------- |
|
Definition
Rise/Run
-----------
y2-y1/x2-x1
-------------- |
|
|
Term
What is the point of a function that crosses the y-axis?
----------------- |
|
Definition
The y-intercept
-------------- |
|
|
Term
At the y-intercept of a function, what does x equal?
------------------ |
|
Definition
|
|
Term
What is the point of a function that crosses the x-axis?
----------------- |
|
Definition
The x-intercept
-------------- |
|
|
Term
At the x-intercept of a function, what does y equal?
------------------ |
|
Definition
|
|
Term
What is the Integral Notation Used for a number not included?
----------------- |
|
Definition
An open circle on a numberline
----------------------
Parenthesis when writing the point
-----------------------
Parenthesis on a number line
-------------------- |
|
|
Term
What is the Integral Notation Used for a number is included?
----------------- |
|
Definition
A closed circle on a numberline
----------------------
Bracket when writing the point
-----------------------
Bracket on a number line
-------------------- |
|
|
Term
When the Slope of the function is positive, what does that mean about the derivative of the function?
----------------- |
|
Definition
The derivative of the function is positive
------------ |
|
|
Term
When the Slope of the function is negative, what does that mean about the derivative of the function?
----------------- |
|
Definition
The derivative of the function is negative
------------ |
|
|
Term
When a piece of a function has a slope of zero aka is a horizontal line, it is considered a what?
------------------------- |
|
Definition
|
|
Term
How do you do a first derivative test (find the behavior of a function analytically without plotting it)?
--------------------- |
|
Definition
1.) Take the Derivative of the Function
----------------------
2.) Set the Derivative Function to Equal Zero and solve it for "x"
2a.) Factor it further to where you have multiple values of "x"
or
2b.) Use the Quadratic Formula to Obtain Multiple Values For "x"
-------------------------
3.) Use the multiple values of "x" you have found, and set a test value between -infinity and your first value, your first value and your second value, and your second value and positive infinity. Represent this information as a chart.
-------------------------------
4.) Substitute your test values into the derivative in place of "x" and mark whether the solution to each value is positive or negative and whether the function is increasing or decreasing on your chart
------------------------
5.) Your x-values are the critical points, mark whether they are maximums or minimums depending on whether or not the slope right before the function is positive or negative
------------------------- |
|
|
Term
|
Definition
A'(x)B(x)+B'(x)A(x)
---------------- |
|
|
Term
(A(x)/B(x))'=
------------ |
|
Definition
A'(x)B(x)-B'(x)A(x)/B(x)^2
---------------- |
|
|
Term
What is Quadratic Formula?
--------------- |
|
Definition
x= (-b(+or-)(sqrt(b^2-4ac)))/2a
----------------------- |
|
|
Term
When given the "x" value for a function, how can you solve for the "y" value of the function?
------------------------ |
|
Definition
Plug the "x" value into the function and solve for the "y" value of the function
--------------- |
|
|
Term
|
Definition
(x-2)(x+2)
Because it has to generate two x-equations made up of factors of "4" that when added together equal zero
---------- |
|
|
