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AP Calculus Derivatives Review Flashcards | StudBud
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AP Calculus Derivatives Review
AP Calculus Derivatives Review
10 terms
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Power Rule and Graphs of Derivatives
Flashcards
10 cards
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Practice quiz
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Questions
10
Answers
1
Find the derivative of f(x) = 7x
-1
f ' (x) = -7x-2
f ' (x) = 7x-2
f ' (x) = -7x
f ' (x) = -7x-1
2
Determine the x-value(s), if any, at which f (x) = x
3
+ 6x - 2 has a horizontal tangent.
x = 2
The graph has no horizontal tangents
x = 3
x = -2
3
Let f (x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
24
-16
-24
16
4
Find the derivative of f(x) = x
4
+ 5x
f ' (x) = 4x2 + 5
f ' (x) = 12x3 + 5x
f ' (x) = 4x3
f ' (x) = 4x3 + 5
5
Find the average rate of change of f(x) = x
2
+ 2x over the interval (1, 2)
6
5
7
4
6
Find the derivative of f(x) = 4x
1/
2
+ 2
f ' (x) = 2x-1/2
f ' (x) = 8x-1/2 + 2
f ' (x) = 8x-1/2
f ' (x) = 2x1/2
7
At which x - value(s) is the graph shown not differentiable?
x = -2 and x = 2
x =1
x = 0
x = 0 and x =1
8
Given f (x) = x
4
+ x
3
- x + 1, what is f ' (1) ?
8
7
6
2
9
Let f (x) = 6x
1/2
. What is the instantaneous rate of change at x = 4?
3/2
6
3
3/4
10
Let f (x) = x
4
+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
7
4
3
10
