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Derivatives and Antiderivatives
Derivatives and Antiderivatives
25 terms
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Just a really fun AP Calculus quiz about derivatives and antiderivatives.
Flashcards
25 cards
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Questions
25
Answers
1
Find the derivative of f(x)= sin(x
2
-5)
f '(x)= -2x⋅cos(x2-5)
f '(x)= 2x⋅cos(x2-5)
f '(x)= -2x⋅sin(x2-5)
f '(x)= 2x⋅sin(x2-5)
2
Find f '(2) if f(x)=x
3
-4x
16
20
22
24
3
Find the derivative of f(x)= tan(sec(x))
sec2(x)⋅sec(sec(x))
tan(x)⋅sec(x)⋅sec2(sec(x))
tan(x)⋅sec2(sec(x))
sec2(tan(x)⋅sec(x))
4
Evaluate ∫ (x÷(x
2
+7))
dx
2⋅ln(x2+7) + C
(1/2)⋅ln(2x) + C
(1/2)⋅ln(x2+7) + C
2x⋅ln(x2+7) +C
5
If f(x)=x
4
+x
3
-2x
2
+x-5, find f ''(2)
68
56
60
48
6
Find the derivative of f(x)= tan(4x
3
+7)
f '(x)= (4x3+7)(sec2(4x3+7))
f '(x)= 12x2(sec2(4x3+7))
f '(x)= 4x3(tan(4x3+7))
f '(x)= 4x3(sec2(4x3+7))
7
If
f(x)
represents the velocity of a particle, what does
∫
|
f(x)
|
dx
represent?
Total Distance
Speed
Acceleration
Displacement
8
If the graph of f(t) represents the position of a particle, what does f "(t) represent?
Instantaneous Velocity
Average velocity
Acceleration
Total Distance
9
If f(x) represents the acceleration of a particle, what does ∫ f(x)
dx
represent?
Displacement
Distance
Speed
Velocity
10
Evaluate ∫ -2x
-3
dx
6x-4 + C
(1/2)⋅x-4 + C
x2 + C
x-2 + C
11
Evaluate ∫ 6x
2
-4x+3
dx
12x-4
6x3-4x2+3x+C
2x3-2x2+3x+C
12x-4+C
12
If f(x)= cos(x) , what is f "(π)?
0
-1
1/2
1
13
Who is our favorite AP Calc teacher?
Definitely Mrs. Damrow
Mrs. Damrow
14
If f(x)=e
2x
,what is f ''(x)?
4e2x
2e2x
2ex
e2x
15
Find f '(x) if f(x)=(5x
5
+5)(-2x
5
-3)
f '(x)= -(10x10+25x5+15)
f '(x)= 10x4(4x5+5)
f '(x)= -10x4(4x5+5)
f '(x)= -25x4(4x5+5)
16
Find the average value of the function f(x)=8x
3
+6x
2
-4x+3 on the interval [0,2]
48
23
25
46
17
If f(x)= (x
2
+3)÷(2x-1) , what is f '(1)?
6
-6
4
-4
18
Evaluate ∫ sin(x)
dx
-cos(x) + C
cos(x)
-cos(x)
cos(x) + C
19
Find the derivative of f(x)=(x
3
+x+1)(x
4
+x
2
+1)
f '(x)= 7x6+10x4+4x3+6x2+2x+1
f '(x)= 10x6+7x4+4x3+6x2+x+2
f '(x)= 7x6+10x4+6x3+4x2+2x+1
f '(x)= 10x6+7x4+4x3+6x2+2x+1
20
Find f "(3) if f(x)= x
3
-2x
2
+7x-4
22
14
8
16
21
Evaluate ∫ 54x
2
+72x-12
dx
16x3+36x2-12x+C
18x3+32x2+12x+C
18x3+36x2-12x+C
16x3+32x-12+C
22
Find the derivative of f(x)= (x
2
+1)÷x
f '(x)= x2+1
f '(x)= 2x-2+1
f '(x)= 2x
f '(x)= 1+x-2
23
Evaluate ∫ sec
2
(2x)
dx
(1/2)⋅tan(2x) + C
2⋅tan(2x) + C
(1/2)⋅tan(x) + C
2⋅tan(x) + C
24
What is the derivative of the function f(x)=x
4
-7x
3
+2x
2
+14
f '(x)= 4x4-21x+4
f '(x)= 4x3+21x2+4
f '(x)= 4x3-21x2+4x
f '(x)= 4x3-7x2+4x
25
Evaluate ∫ x
-1
dx
ex +C
ln(x)
ln(x) + C
e-x +C
