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AP Calculus Basic Derivatives Flashcards | StudBud
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AP Calculus Basic Derivatives
AP Calculus Basic Derivatives
16 terms
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Power Rule and Graphs of Derivatives
Flashcards
16 cards
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Questions
16
Answers
1
Find the derivative of f(x) = x
4
+ 5x
f ' (x) = 4x2 + 5
f ' (x) = 12x3 + 5x
f ' (x) = 4x3
f ' (x) = 4x3 + 5
2
Find the derivative of f(x) = 4x
1/
2
+ 2
f ' (x) = 2x1/2
f ' (x) = 8x-1/2
f ' (x) = 2x-1/2
f ' (x) = 8x-1/2 + 2
3
Given the graph of V(t) of a moving object. When is the object moving RIGHT?
(4,8)
(0,9)
(0,2)
(2,4) & (8,10)
4
Find the derivative of f(x) = 7x
-1
f ' (x) = 7x-2
f ' (x) = -7x-1
f ' (x) = -7x-2
f ' (x) = -7x
5
Given the graph of f ' (x), on what interval(s) is f decreasing?
(4, 6)
(3, 5)
(0, 2) and (3, 5)
(0, 4)
6
Given the graph of V(t) of a moving object. When is the object speeding up?
(4,8)
(0,2) & (9,10)
(2,4) & (8,9)
(2,4) & (8,10)
7
Let f (x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
24
-16
-24
16
8
Let f (x) = x
4
+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
3
7
10
4
9
Let f (x) = 5x
2
. Find an equation of the tangent line to f(x) at x = 2.
y-40 = 20 (x-2)
y-20 = 10 (x-2)
y-10 = 10 (x-2)
y-20 = 20 (x-2)
10
Let f (x) = 6x
1/2
. What is the instantaneous rate of change at x = 4?
3
3/2
3/4
6
11
S(t) = (x + 3)(2x - 5) find V(t)
v(t) = 2x2 + x - 15
v(t) = 2x + 1
v(t) = (2x - 5) + 2(x+3)
v(t) = 2
12
what is acceleration?
s''(t)
dv / dt
v'(t)
all of the above
13
Given S(t) = t
4
+ t
3
- t + 1, what is V(1) ?
2
7
6
8
14
Given the graph of V(t) of a moving object. When is the acceleration positive?
(2,4) & (8,10)
(0,9)
(0,2)
(4,8)
15
Given the graph of f ' (x), on what interval(s) is f(x) decreasing?
(10, 15)
(5, 12.5)
(12.5, 20)
(0, 10) and (15, 20)
16
y = AB find y'
y' = AB' + A'B
y' = A'B'
y' = A'B + AB'
y' = A'B - AB'
