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AP Calculus Basic Derivatives (with e) Flashcards | StudBud
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AP Calculus Basic Derivatives (with e)
AP Calculus Basic Derivatives (with e)
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Power Rule and Graphs of Derivatives
Flashcards
13 cards
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Practice quiz
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Questions
13
Answers
1
Given f (x) = x
4
+ x
3
- x + 1, what is f ' (1) ?
2
8
6
7
2
Given the graph of f ' (x), on what interval(s) is f decreasing?
(3, 5)
(0, 4)
(0, 2) and (3, 5)
(4, 6)
3
Find the derivative of y = 1/x
3
y'=-3x4
y'=-3x-2
y'=-3x-4
y'=3x4
4
Find the derivative of f(x) = 7x
-1
f ' (x) = 7x-2
f ' (x) = -7x
f ' (x) = -7x-1
f ' (x) = -7x-2
5
Let f (x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
-24
24
-16
16
6
Find the derivative of f(x) = x
4
+ 5x
f ' (x) = 4x3
f ' (x) = 4x3 + 5
f ' (x) = 12x3 + 5x
f ' (x) = 4x2 + 5
7
Given the graph of f ' (x), on what interval(s) is f(x) decreasing?
(12.5, 20)
(10, 15)
(5, 12.5)
(0, 10) and (15, 20)
8
Find the derivative of f(x) = 5xe
x
f'(x) = 5ex + 5x
f'(x) = 5xex + 5ex
f'(x) = 5xex
f'(x) = 5ex
9
Find the derivative of f(x) = 4x
1/
2
+ 2
f ' (x) = 8x-1/2
f ' (x) = 2x-1/2
f ' (x) = 2x1/2
f ' (x) = 8x-1/2 + 2
10
Let f (x) = 6x
1/2
. What is the instantaneous rate of change at x = 4?
3
6
3/2
3/4
11
Let f (x) = x
4
+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
10
4
7
3
12
Find the derivative of y = 3 tan x - sin x
y' = 3 sec2x - cos x
y' = 3 sec2x - sin x
y' = 3 sec2x + cos x
y' = 3 csc2x - cos x
13
Let f (x) = 5x
2
. Find an equation of the tangent line to f(x) at x = 2.
y-10 = 10 (x-2)
y-40 = 20 (x-2)
y-20 = 10 (x-2)
y-20 = 20 (x-2)
