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AP Calc_Chapter 3 Review Flashcards | StudBud
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AP Calc_Chapter 3 Review
AP Calc_Chapter 3 Review
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A #math #calculus review of derivatives and basic derivative rules
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Answers
1
What is the derivative of a constant?
c
x
1
0
2
How do we find the jerk?
second derivative of displacement
set v(t) = 0
derivative of acceleration
derivative of velocity
3
What is the derivative of displacement called?
instantaneous rate of change
jerk
acceleration
velocity
4
Derivative does not exist in all these
except
:
vertical tangent
cusp
corner
horizontal tangent
5
Find the derivative of f(x)=3x(x-3)
f'(x)=6x-9
f'(x)=-9
f'(x)=3x
f'(x)=3x2+9
6
find f'(2) for f(x)=4x
3
-5x
2
+2
28
48
10
0
7
when does the particle change directions if s(t)=2t
2
+18
t=1
t=0
t=3
t=9
8
find f'(x) for f(x)=3x
6
+5x
2
-3
f'(x)=12x2+10x+3
f'(x)=18x5+10x
f'(x)=10x5-18x
f'(x)=18x5-10x
9
what is f'(x) if f(x)=3xsin(x)
f'(x)=3xcos(x)+3sin(x)
f'(x)= 3cos(x)
f'(x)=3xcos(x)-3sin(x)
f'(x)=3sin(x)
10
What is the power rule of derivatives?
y' = nxn-1
y' = uv'+u'v
y' = nxn
y' = 0
11
Find y' if y = cos(x)
y' = 0
y' = sin(x)
y' = -sin(x)
y' = cos2(x)
12
what is the general equation of displacement?
s(t) = v'(t)
s(t) = 1/2gt2-v0t+s0
s(t) = 1/2gt2
s(t) = 1/2gt2+v0t+s0
13
what is the product rule?
y' = uv'+vu'
y' = nxn-1
y' = u / v'
y' = vu' - uv'
14
In motion - how do we know when a particle is changing directions?
v(0)
a(t)=0
s(t)=0
v(t)=0
15
How does f'(x) behave when f(x) is decreasing?
f'(x)>0
f'(x)=0
f'(x)=c
f'(x)<0
16
what is the acceleration at t=2 for s(t)=2x
2
+2x-7
0
-7
8
4
17
what does a negative velocity indicate?
nothing
object is still
object is moving backwards (or left)
object is moving forwards (or right)
18
what is speed?
|a(t)|
|v(t)|
v(t)
|s(t)|
19
when does the particle change directions if v(t)=4t-8
t=2
t=4
never
t=0
20
How do we find horizontal tangents of f(x)
f'(x)=0
f(x)=0
f(0)
f'(0)
21
How do we get acceleration?
Take derivative of velocity
take derivative of displacement
absolute value of velocity
multiply displacement
