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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
20 terms
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This is a chapter review game for derivatives in a Calculus BC class.
Flashcards
20 cards
F
Practice quiz
P
Host live
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Questions
20
Answers
1
What rule is represented by d/dx (8) = 0?
product rule
constant rule
chain rule
sum rule
2
If a particle's position is represented by s(t)=t
2
-4t+3, find the acceleration at t=3
1/2
does not exist
6
2
3
If y=ln(x
2
), find y'.
2x2
2/x2
2/x
2
4
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)
5
Which of the following is not true about the derivatives of trig functions?
d/dx tan(x) = sec2(x)
d/dx sin(x) = -cos(x)
d/dx cos(x) = -sin(x)
d/dx sec(x) = sec(x)tan(x)
6
Which of the following represents the power rule?
d/dx(xn) = (n) / (xn)
d/dx(xn) = nxn+1
d/dx(xn) = nxn-1
d/dx(xn) = (n-1)xn
7
Find y'', the second derivative, for y = x
3
-5x
2
+2
6
6x-10
does not exist
3x2-10x
8
Which of the following is not true about the derivatives of exponential and log functions?
d/dx ex = exln(x)
d/dx ln(x) = 1/x
d/dx ex = ex
9
Who is responsible for discovering Calculus?
Mrs. Grossman
Issac Newton and Gottfried Wilhelm von Leibniz
Gottfried Wilhelm von Leibniz
Issac Newton
10
Who is the best AP Calculus teacher at Pittsville High School [hint: see the picture below]?
Mrs. Grossman
Mrs. G.
All of the above
11
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)] / h
All of the above
limit as x approaches 0 of [f(x+h) - f(x)] / h
limit as h approaches 0 of [f(x+h) + f(x)] / x
12
For the graph below, does f'(0) exist?
yes
no
13
If a particle's position is represented by s(t)=(t
2
-4t+3) / (t+1), find the velocity at t=2
9
1/9
1/3
2/9
14
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)]
4sin3(x)sec2(4x)
1
15
Which of the following are NOT proper notations for the derivative of f(x) or y
y'
dx/dy
f'(x)
df/dx
16
Why is the function y = (x)
2/3
not differentiable at x=0?
cusp
discontinuity
corner
vertical tangent
17
Find dr/dx for r = tan(2 - x)
sec2(2-x)*(2-x)
sec2(2-x)
-sec2(2-x)
-tan(2-x)
18
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+3x
5x4+6x
5x4+3x2+6x
5x-3x2+6
19
If f has a derivative at x=a, then f is continuous at x=a.
True
False
20
Find f'(4) the derivative of f(x)=x
3
48
64
12
24
