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AP Calculus Applications of Derivatives Flashcards | StudBud
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AP Calculus Applications of Derivatives
AP Calculus Applications of Derivatives
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Ch 3
Flashcards
23 cards
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Practice quiz
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Questions
23
Answers
1
For any continuous function f(x) on the interval a<x<b, if f
'
(x)<0, then
f(x) is concave down
f(x) is concave up
f(x) is decreasing
f(x) is increasing
2
For any continuous function f(x) on the interval a<x<b, if f
''
(x)>0, then
f(x) is increasing
f(x) is concave up
f(x) is concave down
f(x) is decreasing
3
The graph of f
'
(x) is shown. Therefore, f(x) is concave down on which interval
x < -2
x > 0
x > -2
x < -4
4
The limit of f(x) = (6x
3
+4x) / (-2x-x
3
) as x→∞ is
6
-6
the limit does not exist
-3
5
The graph of f
'
(x) is shown. Therefore, f(x) has a local minimum at
f(x) has no local minimum
x = -4
x = 0
x = -2
6
For any continuous function f(x) on the interval a<x<b, if f
''
(x)<0, then
f(x) is increasing
f(x) is concave up
f(x) is decreasing
f(x) is concave down
7
The graph of f
'
(x) is shown. Therefore, f(x) is decreasing on which interval?
-4 < x < -2
x > -4
-4 < x < 0
x < -4
8
The y-value of which point represents a relative maximum of f(x)
F
A
D
C
9
For 1<c<3, if f(1) = 9 and f(3) = 7, then MVT guarantees that
f'(c) = 1
f'(c) = -1
f'(c) = 0
f'(c) is undefined
10
The absolute maximum value of f(x) on the interval [a,b] is
the y value of point B
the y value of point F
the x value of point B
the x value of point F
11
The M.V.T. states that if a function is continuous and differentiable on [a,b] , then for a<c<b
f'(c) = (f(b) - f(a)) / (b - a)
f'(c) is undefined
f'(c) = 0
bananas?
12
The Extreme Value Theorem states if a ƒ is continuous on an interval [a,b], then
there must exist a derivative of ƒ = 0
ƒ must be differentiable
there must exist a maximum value of ƒ
there must exist a minimum value of ƒ
13
The limit of f(x) = (6x
3
+4x) / (-2x-x
2
) as x→∞ is
-6
the limit does not exist
6
-3
14
The graph of f
'
(x) is shown. Therefore, f(x) is increasing on which interval?
-4 < x < 0
x < 2
x > 2
-4 < x < -2
15
If f
''
(x) > 0 for all values of x and L(x) is the tangent line at the point (x, f(x)), then
there is not enough information to determine f(x) values
L(x) will be neither an underestimate nor overestimate
to approximate f(x) values, L(x) is an underestimate
to approximate f(x) values, L(x) is an overestimate
16
The y-value of which point represents a relative minimum of f(x)
D
A
C
B
17
For any continuous function f(x) on the interval a<x<b, if f
'
(x)>0, then
f(x) is increasing
f(x) is concave up
f(x) is concave down
f(x) is decreasing
18
The absolute minimum value of f(x) on the interval [a,b] is
the y value of point A
the x value of point C
the x value of point A
the y value of point C
19
The graph of f
'
(x) is shown. Therefore, f(x) has a local maximum at
f(x) has no local maximum
x = -4
x = -2
x = 0
20
The graph of a function f(x) is shown. f(x) appears to have an inflection point at
x = 3.75
x = 2
x = -2.5
x = 0
21
The limit of f(x) = (6x
3
+4x) / (-2x
4
+x
3
) as x→∞ is
0
6
the limit does not exist
-3
22
The graph of f
'
(x) is shown. Therefore, f(x) is concave up on which interval
x > -2
x < -4
x < -2
x > 0
23
The graph of f
'
(x) is shown. Therefore, f(x) has an inflection point at
x = -4
x = 0
f(x) has no inflection point
x = -2
