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Duplicate of Chapter 3 Review: Derivatives Flashcards | StudBud
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Duplicate of Chapter 3 Review: Derivatives
Duplicate of Chapter 3 Review: Derivatives
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This is a chapter review game for derivatives in a Calculus BC class.
Flashcards
29 cards
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Practice quiz
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Questions
29
Answers
1
The derivative of the function f(x) is represented by which of the following definitions?
limit as h approaches 0 of [f(x+h) + f(x)] / x
limit as x approaches 0 of [f(x+h) - f(x)] / h
limit as h approaches 0 of [f(x+h) - f(x)] / h
All of the above
2
Find an equation for the line tangent to the curve f(x)= (x
3
+1) / (2x) at x=1
y - 1 = 1/2(x - 1)
y = 1/2(x - 1)
y = 1/3(x + 3)
y - 2 = 1/3(x - 2)
3
Which of the following is not true about the derivatives of inverse trig functions?
d/dx arctan(x) = 1 / (1+x2)
d/dx arcsin(x) = 1 / [sqrt(1-x2)]
d/dx arccos(x) = -1 / [sqrt(1-x2)]
d/dx arcsec(x) = 1 / [ |x|(x2-1) ]
4
Which of the following represents the power rule?
d/dx(xn) = nxn+1
d/dx(xn) = nxn-1
d/dx(xn) = (n) / (xn)
d/dx(xn) = (n-1)xn
5
Which of the following is not a derivative rule?
difference rule
constant multiple rule
second derivative rule
sum rule
6
Which of the following is not true about the derivatives of exponential and log functions?
d/dx ln(x) = 1/x
d/dx ax = axln(a)
d/dx logax = ln(a) / x
d/dx ex = ex
7
If y=ln(x
2
), find y'.
2/x2
2
2x2
2/x
8
Find y' for y=x
2
e
x
- xe
2x
ex(x2+2x)
ex(x2+2x)-e2x(2x+1)
1
3ex(x2+2x)-7e2x(2x+1)
9
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+3x
5x4+3x2+6x
5x4+6x
5x-3x2+6
10
Which of the following is not true about the derivatives of trig functions?
d/dx cot(x) = -csc2(x)
d/dx sin(x) = cos(x)
d/dx csc(x) = csc(x)cot(x)
d/dx tan(x) = sec2(x)
11
What rule is represented by d/dx (8) = 0?
sum rule
chain rule
constant rule
constant multiple rule
12
The function y = (x)
2/3
fails to be differentiable at x=0, what type of problem is at x=0?
cusp
vertical tangent
corner
discontinuity
13
If a particle's position is represented by s(t)=(t
2
-4t+3) / (t+1), find the velocity at t=2
1/3
9
1/9
2/9
14
Use the limit of the difference quotient to determine the derivative of f(x)=x
3
3x3
3x2
3x2+3h
x3+x+h
15
All of the following are proper notations for the derivative f(x), f(x) is replaceable by y
df/dx
dy/dx
d/dx
y'
16
Find y'', the second derivative, for y = x
3
-5x
2
+2
6x-10
3x2-10x
does not exist
6
17
Find y' for y=sin
3
(x)tan(4x)
sin2(x) + 4sin(x) - 3cos(x)
sin2(x) [3cos(x)tan(4x) + 4sin(x)sec2(4x)]
1
4sin3(x)sec2(4x)
18
Which of the following is true about the domains of a function and its derivative f'(x)?
domain f(x) is greater than or equal to the domain f'(x)
domain f(x) is less than or equal to the domain f'(x)
19
Who is your favorite AP Calculus teacher??
Mr. Bowden
Mrs. Colbeth
20
Find y' for y=sin
-1
(1-t)
y' does not exist
1
-1 / sqrt(2t-t2)
1 / (2t-t2)
21
If f has a derivative at x=a, then f is continuous at x=a.
True
False
22
For the graph below, does f'(0) exist?
no
yes
23
Which of the following is not true about the derivatives of trig functions?
d/dx tan(x) = sec2(x)
d/dx sec(x) = sec(x)tan(x)
d/dx sin(x) = -cos(x)
d/dx cos(x) = -sin(x)
24
Find dy/dx for xsin(2y) = ycos(2x)
[-2ysin(2x)-sin(2y)]*[cos(2x)]
dy/dx does not exist
1
[-2ysin(2x)-sin(2y)]/[2xcos(2y)-cos(2x)]
25
If a particle's position is represented by s(t)=t
2
-4t+3, find the acceleration at t=3
1/2
6
does not exist
2
26
Find dy/dx for y = (x) / (1 + cos(x))
[1] / [1+2cos(x)+cos2(x)]
[1+cos(x)+xsin(x)]
[1+cos(x)+xsin(x)] / [1+2cos(x)+cos2(x)]
[1-cos(x)+3xsin(x)] / [1+2cos(x)+cos2(x)]
27
If x(t)=t
2
+t and y(t)=sin(t), find dy/dx as a function of t.
sin(t) / (2t +1)
cos(t) / 2t
cos(t)*(2t +1)
cos(t) / (2t +1)
28
Find dr/dx for r = tan(2-x)
sec2(2-x)*(2-x)
sec<font size="2">2(2-x)</font>
-sec2(2-x)
-tan(2-x)
29
Using implicit differentiation, find dy/dx for x
2
- xy + x
2
= 7
dy/dx = (y-2x) / (2y-x)
dy/dx = (y^2) / (-2x + y)
dy/dx = 1
none of the above
