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AP Calculus Basic Derivatives Flashcards | StudBud
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AP Calculus Basic Derivatives
AP Calculus Basic Derivatives
20 terms
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Power Rule and Graphs of Derivatives
Flashcards
20 cards
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Questions
20
Answers
1
If function changes from increasing to decreasing, what does that mean?
There is a local maximum
There is an inflection point
There is a horizontal asymptote
There is a critical number
2
Let f (x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
16
24
-24
-16
3
How do we find critical numbers?
Find the 2nd derivative and set it equal to zero
Set the function equal to zero
Find the 1st derivative and set it equal to zero
Do chain rule to both sides
4
What is the formula for volume of a sphere?
(4/3)πr3
(1/3) πr2h
(2/3)πr3
πr2
5
Find the derivative of f(x) = 4x
1/
2
+ 2
f ' (x) = 2x1/2
f ' (x) = 8x-1/2 + 2
f ' (x) = 8x-1/2
f ' (x) = 2x-1/2
6
Find the derivative of f(x) = 7x
-1
f ' (x) = 7x-2
f ' (x) = -7x-2
f ' (x) = -7x-1
f ' (x) = -7x
7
Find the derivative of f(x) = x
4
+ 5x
f ' (x) = 4x2 + 5
f ' (x) = 4x3
f ' (x) = 4x3 + 5
f ' (x) = 12x3 + 5x
8
Find the critical numbers: f(x) = 2x
3
- 3x
2
- 12x
x = 6, x = 2, x = 1
x= 6, x = 2, x = -1
x = 2, x = -1
x = -2, x = 1
9
At which x - value(s) is the graph shown not differentiable?
x =1
x = 0
x = -2 and x = 2
x = 0 and x =1
10
Let f (x) = x
4
+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
7
3
4
10
11
lim x →∞ (1 / x)
2
∞
0
1
12
Find the derivative of sin(x)
sec2(x)
cos(x)
-cos(x)
cos2(x)
13
Find the derivative of tan (x)
cot2(x)
sec2(x)
tan(x) sec(x)
sec(x)
14
Determine the x-value(s), if any, at which f (x) = x
3
+ 6x - 2 has a horizontal tangent.
The graph has no horizontal tangents
x = 2
x = -2
x = 3
15
Let f (x) = 6x
1/2
. What is the instantaneous rate of change at x = 4?
3/4
3/2
6
3
16
Given f (x) = x
4
+ x
3
- x + 1, what is f ' (1) ?
8
7
2
6
17
If concavity changes from up to down, what does that mean?
There is an inflection point
There is a critical number
There is a local maximum
There is a horizontal asymptote
18
Find the average rate of change of f(x) = x
2
+ 2x over the interval (1, 2)
4
6
5
7
19
Find the second derivative of f(x) = 4x
2
- 10x + 23
8x
-8
6
8
20
Volume of a cylinder
(1/2)πr2h
πr2
πr3h
πr2h
