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Ch.4 & 11 Derivatives Review Flashcards | StudBud
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Ch.4 & 11 Derivatives Review
Ch.4 & 11 Derivatives Review
21 terms
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#calculus #derivatives
Flashcards
21 cards
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Questions
21
Answers
1
All of the following are proper notations for the derivative f(x), f(x) is replaceable by y
d/dx
y'
dy/dx
df/dx
2
Find an equation for the line tangent to the curve f(x)= (x
3
+1) / (2x) at x=1
y = 1/3(x + 3)
y = 1/2(x - 1)
y - 2 = 1/3(x - 2)
y - 1 = 1/2(x - 1)
3
Who is responsible for discovering Calculus?
Issac Newton
Mrs. Mascotti
Issac Newton and Gottfried Wilhelm von Leibniz
Gottfried Wilhelm von Leibniz
4
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
2/9
1/9
5
Find dy/dx for xsin(2y) = ycos(2x)
[-2ysin(2x)-sin(2y)]/[2xcos(2y)-cos(2x)]
dy/dx does not exist
[-2ysin(2x)-sin(2y)]*[cos(2x)]
1
6
Using implicit differentiation, find dy/dx for x
2
- xy + x
2
= 7
dy/dx = 1
dy/dx = (y-2x) / (2y-x)
none of the above
dy/dx = (y^2) / (-2x + y)
7
Using left and right handed derivatives, does the derivative at x=0 exist for the function...
yes, y'(0) = 0
No, f'(0) does not exist
yes, because the function is defined at x=0
yes, y'(0) = 2
8
Find y'', the second derivative, for y = x
3
-5x
2
+2
6x-10
6
does not exist
3x2-10x
9
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+3x
5x-3x2+6
5x4+3x2+6x
5x4+6x
10
For the graph below, does f'(0) exist?
yes
no
11
Which of the following represents the power rule?
d/dx(xn) = (n-1)xn
d/dx(xn) = nxn-1
d/dx(xn) = (n) / (xn)
d/dx(xn) = nxn+1
12
The function y = (x)
2/3
fails to be differentiable at x=0, what type of problem is at x=0?
corner
vertical tangent
discontinuity
cusp
13
Use the limit of the difference quotient to determine the derivative of f(x)=x
3
3x2+3h
3x3
x3+x+h
3x2
14
Which of the following is not a derivative rule?
constant multiple rule
sum rule
difference rule
second derivative rule
15
Which of the following is not true about the derivatives of trig functions?
d/dx tan(x) = sec2(x)
d/dx csc(x) = csc(x)cot(x)
d/dx cot(x) = -csc2(x)
d/dx sin(x) = cos(x)
16
Find dr/dx for r = tan(2-x)
-sec2(2-x)
sec2(2-x)
sec2(2-x)*(2-x)
-tan(2-x)
17
If x(t)=t
2
+t and y(t)=sin(t), find dy/dx as a function of t.
cos(t) / 2t
sin(t) / (2t +1)
cos(t)*(2t +1)
cos(t) / (2t +1)
18
If f has a derivative at x=a, then f is continuous at x=a.
True
False
19
What rule is represented by d/dx (8) = 0?
constant rule
chain rule
sum rule
constant multiple rule
20
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)
21
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
