Misc
Inc/Dec
Minimums
Maximums
Concavity
100
What are critical numbers?
Where x is 0 or undefined.
100
When is f(x) decreasing on an interval?
When f'(x) is negative.
100
What is a minimum?
A place where f(x) goes from decreasing to increasing?
100
What is a maximum?
A place where f(x) goes from increasing to decreasing?
100
The Second Derivative Test.
What is the test used to find concavity?
200
What are exremas?
The maximums and minimums.
200
IF f'(x) > 0 for all x in an interval then what is happening to f(x)?
f(x) is increasing.
200
What is the minimum of x^2?
At x=0.
200
What is the absolute maximum of x^2?
There is none, undefined.
200
What is an inflection point?
Where f(x) changes concavity.
300
What is the difference between relative and absolute min/max?
Relative is an area and there could be multiple while there is only one absolute.
300
What is the name of the process used to figure out if a function is increasing or decreasing?
The First Derivative Test.
300
What is the process used to find absolute minimum?
The Candidate Test.
300
How do you find what is a maximum when given a graph?
Look for when the function is increasing then decreasing.
300
If f''(x) < 0 for all x in an interval what is happening to f(x)?
f(x) is concave down.
400
In the Candidate Test what can be used as critical numbers?
Endpoints and where x is zero or undefined.
400
Describe the slope of a linear function.
It is always increasing or decreasing.
400
What is the absolute minimum of of -x^2 on the integral (-10,10)?
-100
400
What is is the relative maximum of the parent cubic function?
There is none.
400
In the Second Derivative Test what are the inflection points?
It is a critical number where f''(x) changes from being positive to negative or vice versa.
500
Find the the absolute maximums and minimum of f(x)=cos(x). (Y-values only)
1 and -1
500
What is the interval in which the parent function x cubed increases and decreases.
It is always increasing.
500
Where is a minimum at x^3-6x^2+9x+6 on the interval of (-1,8)?
At x=3 there is a minimum.
500
What is the relative and absolute maximum of a the parent linear function?
There is no relative and the absolute is infinity.
500
If f(x) is concave up on the interval (-2,2) and f(x) has a line of symmetry at x=0 , what is happening to f'(x)?
f'(x) is negative on the interval (-2,0) and is positive on the interval (0,-2).
M
e
n
u