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AP Calculus Review For Fall Final- Derivatives Pt 2 Flashcards | StudBud
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AP Calculus Review For Fall Final- Derivatives Pt 2
AP Calculus Review For Fall Final- Derivatives Pt 2
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#derivativegraphs #particlemotion #implicitdifferntiation
Flashcards
19 cards
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Questions
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Answers
1
The first derivative test tells us (select all that apply)
the maximum/minimum of the graph
whether the graph is differentiable
the c value between point A and point B
the interval a function is increasing or decreasing on
2
If the second derivative is negative, then the function is...
concave down
concave up
decreasing
increasing
3
Derivative of position gives ...
direction
acceleration
velocity
speed
4
if a particle changes direction, then
velocity equals zero
acceleration is negative
position equals zero and changes sign
velocity equals zero and changes sign
5
More Implicit Differentiation
D
A
B
C
6
Use the first derivative test to find the following
x=-4
x=-4, 3
x=0
x=3
7
A graph of the velocity of a particle is shown. Where is the particle moving to the right?
(-7, 2)
(-7, -2) U (-2, 5)
(-∞, -7) U (5, ∞)
(2, 5)
8
If the first derivative is positive, then the function is....
negative
decreasing
increasing
positive
9
use the 2nd derivative test
B
D
A
C
10
In what intervals is the second derivative negative? Explain.
(-2, 0) because f' is negative.
(-3, 0) U (1, 3) because f' is concave up.
(-3, -2) U (0,3) because f' is positive.
(-3, -1) U (1,2) because f' is decreasing.
11
If the velocity of the particle is positive, then the particle is _________
moving to the right
moving to the left
not moving
12
At what points on the derivative graphs do maximums occur on the original graphs?
at the x axis where slopes change from negative to positive
at the y axis where slopes change from negative to positive
at the x axis where slopes change from positive to negative
at the y axis where slopes change from positive to negative
13
What can the Second Derivative Test Help Find?
Asymtotes
Points of Inflection
Intercepts
Intervals of Concavity
14
Mean Value Theorem
B
A
C
D
15
1st deriv. graphs
D
B
C
A
16
Match graph (d) with the graph of its derivative.
IV
III
II
I
17
3.6 Curve Sketching
a
c
d
b
18
Derivative of ... gives acceleration.
speed
position
displacement
velocity
19
Intermediate Value Theorem
0
3
1/2
2
