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Derivatives Flashcards | StudBud
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Derivatives
Derivatives
20 terms
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Review game for simple derivatives and differentiation rules used in Calculus
Flashcards
20 cards
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Practice quiz
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Host live
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Questions
20
Answers
1
The slope of the tangent line to the graph of x=sin(y) [y=arcsin(x)] at the point (0,π) is
0
1
-1
not defined
2
True or False: The derivative of ln(π) is 1/π.
True
False
3
Derivative of ln(e
2x
)
2/e2x
2x
2
1/e2x
4
If f'(a) exists, limit as x→a of f(x)
It must exist, but there is not enough info to determine it
it may not exist
equals f'(a)
equals f(a)
5
True or False: If f is not differentiable at x, f is not continuous at x.
False
True
6
Assume that f(x) is continuous on [a,b] and let f(c) be the minimum or maximum value on [a,b].
Then c is one of the endpoints a or b.
Then c=a, that is, the left endpoint.
Then c is a critical point.
Then c is either a critical point or one of the endpoints
7
If h(x)=f
2
(x)-g
2
(x), f'(x)=-g(x), and g'(x)=f(x), then h'(x)=
1
0
-4⋅f(x)⋅g(x)
(-g(x))2-(f(x))2
8
If f(x) is not continuous on [0,1], then
f(x) might not have any extreme values on [0,1]
f(x) has no extreme values on [0,1]
9
If f and g are both differentiable and h(x)=f(g(x)), h'(2) equals
f'(g'(2))⋅g'(2)
f'(g(2))⋅g'(2)
f'(g(x))⋅g'(2)
f'(2)⋅g(2)
10
True or False. The function f(x)=|x| has a derivative at x=0.
True
False
11
True or False: If f is differentiable at x, f is continuous at x.
True
False
12
True or False: If f(c) is a local min or max, then c is a critical point of f(x).
False
True
13
A number c in the domain of f is called a critical point if...
f'(c)=0
either f'(c)=0 or f'(c) does not exit
f'(c) does not exist
14
Let h(x)=f(x)/x
2
. If f(3)=2 and f'(3)=4, then h'(3) is
16/3
8/3
16/27
8/27
15
If g(x)=arcsin(x), then g'(x) is
1/√(1-x2)
-cos(x)/sin2(x)
1/cos(x)
csc(x)⋅cot(x)
16
True or False: If f(x)=ln(3x), f'(x)=1/x
True
False
17
True or False. If f(x)=x
1/3
then f'(0) exists.
True
False
18
If f(x) is continuous but has no critical points in [0,1], then
f(x) has no min or max on [0,1]
Either f(0) or f(1) is the minimum value on [0,1]
19
If f(x)=sin(x) then
all of the above
f'(x)=cos(x)
f(x)=-f''(x)
f(x)=f(4)(x)
20
The derivative of the function f(x)=tan(x
3
) is
none of the above
1+tan2(x3)
x3⋅(1+tan2(x3))
3x2⋅(1+tan2(x3))
