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Derivatives
Derivatives
16 terms
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StudBud Administration
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This is a chapter review game for derivatives in a Calculus BC class.
Flashcards
16 cards
F
Practice quiz
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Host live
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Questions
16
Answers
1
For the graph below, does f'(0) exist?
yes
no
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 = 1/3(x + 3)
y - 2 = 1/3(x - 2)
y = 1/2(x - 1)
3
Find y'', the second derivative, for y = x
3
-5x
2
+2
6
does not exist
6x-10
3x2-10x
4
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
2
6
5
Which of the following is not true about the derivatives of trig functions?
d/dx sec(x) = sec(x)tan(x)
d/dx sin(x) = -cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec2(x)
6
Which of the following are NOT proper notations for the derivative of f(x) or y
y'
dx/dy
df/dx
f'(x)
7
If y=ln(x
2
), find y'.
2/x
2/x2
2x2
2
8
Find dr/dx for r = tan(2 - x)
-sec2(2-x)
sec2(2-x)
-tan(2-x)
sec2(2-x)*(2-x)
9
Which of the following represents the power rule?
d/dx(xn) = (n) / (xn)
d/dx(xn) = (n-1)xn
d/dx(xn) = nxn-1
d/dx(xn) = nxn+1
10
Why is the function y = (x)
2/3
not differentiable at x=0?
corner
discontinuity
cusp
vertical tangent
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)] / x
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)] / h
12
If a particle's position is represented by s(t)=(t
2
-4t+3) / (t+1), find the velocity at t=2
9
2/9
1/3
1/9
13
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+3x
5x4+3x2+6x
5x4+6x
5x-3x2+6
14
If f has a derivative at x=a, then f is continuous at x=a.
False
True
15
Find f'(4) the derivative of f(x)=x
3
64
12
48
24
16
Find y' for y=sin
3
(x)tan(4x)
sin2(x) [3cos(x)tan(4x) + 4sin(x)sec2(4x)]
sin2(x) + 4sin(x) - 3cos(x)
4sin3(x)sec2(4x)
1
