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