Exam 3 Flashcards
(10 cards)
1
Q
concave up on an open interval
A
if f’ is increasing on the interval I
2
Q
concave down on an open interval
A
if f’ is decreasing on the interval I
3
Q
If f is increasing
A
f’ > 0
4
Q
If f is decreasing
A
f’ is less than zero
5
Q
If f is concave up
A
f’’ > 0
6
Q
If f is concave down
A
f’’ is less than zero
7
Q
Define a critical point
A
a point c where f’(c)=0 or f’(c) DNE
8
Q
inflection point
A
a point x=a where f has a tangent line and f changes concavity.
9
Q
How do you find critical points algebraically?
A
ask where f’(x)=0 AND where f’(x) DNE
10
Q
How do you find inflection points?
A
- look for places where f”(x) = 0
- test either side to see if concavity changes
- if concavity changes AND f has a tangent line, then you have an inflection point
