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AP Calculus Derivatives and Limits Basics Flashcards | StudBud
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AP Calculus Derivatives and Limits Basics
AP Calculus Derivatives and Limits Basics
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Derivatives and Limits Review
Flashcards
20 cards
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Practice quiz
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Questions
20
Answers
1
Find the average acceleration of the boat over the interval [5, 10]
4/5 m/s2
1/5 m/s2
2/5 m/s2
3/5 m/s2
2
limit as x → 1 of function shown in graph
0
-1
does not exist
1
3
The position of a particle is given by s(t) = 3x
2
- 7x. Describe its speed at t = 1.
speed is decreasing
speed is increasing
4
Use the values in the table to find the derivative of f(x) g(x) at x = 3
1
3
2
4
5
limit as x → 0 of function shown in graph
1
does not exist
0
2
6
limit as x→3
+
of graph of function
1
- ∞
+ ∞
0
7
The derivative of (cos x) / 2x at t = π
2 / π
2 / π2
2 / 4π2
1 / 4π2
8
The slopes of parallel lines are
never equal
always negative
negative reciprocals
the same
9
Find the slope of y = x
3
at x = 3
1/9
9
27
1/3
10
Find y ' if y = sin x
sec x
tan x
cos x
cot x
11
Given graph of f ' (x), on what interval (s) is f (x) decreasing ?
(-∞, 2) and (3, 5)
(4, 6)
(-∞, 2) and (4, 5)
(2, 4)
12
Find the average rate of change of y = x
2
on [1 , 3]
4
8
6
2
13
Find the velocity function if the position function is s(t) = x
5
+ x
4
- 4x
v(t) = 5 x + 4 x 3 - 4
v(t) = 5 x 4 + 4 x 3 - 4
v(t) = 5 x 4 + 4 x
v(t) = 5 x 4 + 4 x 3
14
Find f ' (x) if f (x) = 3x
4
- 5x
2
+ 8
12x 3 - 10 x
12x - 10 x
12x 3 - 10
12x 2 - 10 x + 8
15
Find the value of x where the tangent line to f(x) = x
2
- 4x is horizontal.
4
1
2
8
16
Find an equation of the tangent line to y = x
2
at x = 3
y - 9 = 3 (x - 3)
y = 6 (x - 3)
y - 3 = 6 (x - 3)
y - 9 = 6 (x - 3)
17
Find y ' (2) if y = 1/x
- 1/2
- 1/4
- 2
- 4
18
Find the instantaneous rate of change of y = x
4
at x = 2.
32
4
16
8
19
The Product Rule states (ab) ' =
a ' b + a b '
2 a ' b '
a ' b '
a b + a ' b '
20
Estimate the acceleration of the boat at t = 12.5 minutes
3 / 5 m/s2
4 / 5 m/s2
13 / 5 m/s2
2 / 5 m/s2
