Critical Points
1st Derivative
2nd Derivative
Sign Diagrams
Max/Mins
100
Find this value by setting a derivative to zero.
What is a critical point?
100
The 1st derivative tells you about this kind of behavior of the graph.
What is "if the graph increases/decreases?"
100
The 2nd derivative tells you this trait of the graph.
What is concavity?
100
the mathematical term for this x=0
What is a critical point?
100
The function's highest value across all possible inputs
What is absolute maximum?
200
Critical Points of:
3x2-3x+2
What is (1/2, 5/4)
200
Graph when f'(x) < 0
Decreases
200
Graph behavior when f''(x) > 0
What is concave up
200
Sign diagrams are most useful for local or absolute points
What is local
200
A point on a function where the output value is less than or equal to all the other output values in a small interval around it
What is a local minimum?
300
Critical Points of:
x2-4x+3
What is (2,-1)
300
Graph when f'(x) > 0
What is increasing
300
Find f''(x)
F(x) = 6x - x2
f''(x) = -2
300
T/F: If the f'(x) sign diagram looks like this, we can assume graph f(x) is concave up from these intervals 
What is false?
300
Find absolute extrema if any of f(x) = 3x - x3 on [-2, 3]
Absolute max is 2
400
Critical Points of:
x3-3x2-9x+5
(-1, 10) and (3, 22)
400
Find f'(x)
F(x) = (x2-4)3
6x(x2-4)2
400
Find f''(x)
F(x) = x2 / (x2+1)
What is (2x(x2-3)) / (x2+1)3
400
If this is a sign diagram for f'(x), what is the behavior of the graph at x = 2?
What is a local minimum?
400
f '(x) = x2 +3x - 8
Identify if max/min using critical points & sign diagram
Local minimum
500
Critical Points of:
(x2-4)7
(-2, 0), (0, -16384), (2,0)
500
f(x) = cos(x2ex) find f'(x)
f'(x) = -(2xex+x2ex)sin(x2ex)
500
Find f''(x) of:
f(x) = ln(x2+1)
(2-2x2)/ (x2+1)2
500
For a sign diagram of f'(x) what is x = -3 on the graph?
What is a local maximum?
500
Find , local extrema, POI, intervals of concavity:
f(x) = x3-12x
EXTRA: DRAW
Local max at x = -2
Local min at x =2
(0,0) = POI
(-inf, 0) concave down
(0, inf) concave up