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Calculus: Derivatives and Concavity Flashcards | StudBud
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Calculus: Derivatives and Concavity
Calculus: Derivatives and Concavity
20 terms
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16 plays
A beginning review of derivatives
Flashcards
20 cards
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Practice quiz
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Questions
20
Answers
1
If f ' (9) < 0 and f '' (9) > 0, at x = 9, the graph of f(x) is?
decreasing and concave down
decreasing and concave up
increasing and concave up
increasing and concave down
2
The derivative of a function is a ________________ calculator.
number
slope
pun
graphing
3
The second derivative of y=sin x is?
cos(x)
-cos(x)
-sin(x)
six(n)
4
What is the derivative of y=xsinx
y'=cosx+xsinx
y'=1cosx
y'=xcosx+sinx
y'=sinxcosx
5
The derivative of 13x
4
is?
42x4
13x3
54x3
52x3
6
If f '(3)=0 and f ''(3)= -1, then at x=3 there is a(n)?
point of inflection
relative min
horse
relative max
7
If f ' (9) < 0 and f '' (9) < 0, at x = 9, the graph of f(x) is?
increasing and concave up
decreasing and concave down
decreasing and concave up
increasing and concave down
8
Where is the point of inflection on the graph of x
3
?
x=0
there isn't one
x=2
infinity
9
If g''(3) = 10, what is happening at x=3?
increasing
concave down
decreasing
concave up
10
If f '' (4) = 0 and f '' (x) changes sign at x = 4, then at x = 4, there is a(n)?
point of inflection
relative max
relative min
rabbit
11
The second derivative of 6x is?
6
0
6x
1
12
If f '(3)=0 and f ''(3)= 0, then at x=3 there is a(n)?
relative max
relative min
horse
point of inflection
13
If f '(3)=0 and f ''(3)=4.5, then at x=3 there is a(n)?
relative min
relative max
point of inflection
horse
14
If g'(3) = 10, what is happening at x=3?
decreasing
concave down
increasing
concave up
15
If f ' (9) > 0 and f '' (9) < 0, at x = 9, the graph of f(x) is?
increasing and concave up
decreasing and concave down
increasing and concave down
decreasing and concave up
16
The derivative of f(x)=sec(8x-3) is?
sec(8x-3)(8)
sec(8x)tan(8x)(8x-3)
sec(8x-3)tan(8x-3)(8)
sec(8x-3)tan(8x-3)(8x)
17
The derivative of f(x)=e
3x-4
is?
ex e3x-4
3xe3x-4
e3x-4
3e3x-4
18
The derivative of g(x)=ln(4x-9) is?
4/(4x-9)
ln(4)(4x-9)
(4x-9)(ln 4)
ln(4x-9)
19
If f ' (1) = -2, what is known about f(x) at x = 1?
decreasing
concave down
concave up
increasing
20
The second derivative of h(x)=e
6x
is?
12ex
12e6x
6e6x
36e6x