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Chapter 3 Review
Chapter 3 Review
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Calculus -- Derivatives
Flashcards
25 cards
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Practice quiz
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Questions
25
Answers
1
This function is not differentiable at x = 0 because . . . .
limx→0- f '(x) ≠ limx→0+ f '(x)
limx→0- f(x) ≠ limx→0+ f(x)
limx→0 f '(x)= ∞
limx→0 f(x)= ∞
2
Differentiate the function below . . .
y' = cotx
y' = secxtanx
y' = -csc2x
y' = sec2x
3
True or False: A function can be differentiable but not continuous at a point.
False
True
4
True or False: AP Calculus is as easy as 3,4,5
True
False
5
Differentiate the function below . . .
y' = -6x
y' = -6x2
y' = -3
y' = -3x3
6
This function is not differentiable at x = 0 because . . . .
limx→0- f(x) ≠ f(0)
limx→0 f '(x)= ∞
limx→0- f(x) ≠ limx→0+ f(x)
limx→0- f '(x) ≠ limx→0+ f '(x)
7
This is the . . . .
Definition of the Derivative
Alternate Definition of the Derivative
Quotient Rule
Power Rule
8
This is the . . . .
Power Rule
Quotient Rule
Definition of the Derivative
Alternate Definition of the Derivative
9
If s(t) is the position function of an object, if the object is speeding up, we need to know if
velocity and acceleration have the same signs
speed is positive
position and velocity have the same signs
velocity and acceleration have different signs
10
Differentiate the function below . . .
y' = sec2x
y' = secxtanx
y' = -cos2x
y' = cscxcotx
11
If s(t) is the position function of an object, a particle is resting when...
position is zero
time is zero
acceleration is zero
velocity is zero
12
Differentiate the function below . . . .
y' = 5x
y' = x4
y' = 4x5
y' = 5x4
13
The graph of the derivative of the function below would look like . . . .
a parabola
a cubic function
a horizontal line
a non-horizontal line
14
True or False: A function can be continuous but not differentiable at a point.
False
True
15
If s(t) is the position function of an object, the first derivative of s(t) is ...
velocity
a headache
speed
acceleration
16
Differentiate the function below . . .
y' = tanx + cotx
y' = cosx - sinx
y' = 7
y' = sinx + cosx
17
The Quotient Rule: "low d-hi minus hi d-low over ______ squared."
x
c
high
low
18
Differentiate the function below . . .
y' = cscxcotx
y' = -cot2x
y' = -sinx
y' = -csc2x
19
This function is not differentiable at x = 0 because . . . .
limx→0- f(x) ≠ f(0)
limx→0- f (x) ≠ limx→0+ f (x)
limx→0 f '(x)= ∞
limx→0- f '(x) ≠ limx→0+ f '(x)
20
To find a horizontal tangent to a function f, take the derivative of f and . . .
set equal to 1
simplify
run
set equal to 0
21
The graph of the derivative of a function f(x) describes the _____ of f(x).
slope
symmetry
life
asymptotes
22
The absolute value of velocity is . . . .
acceleration
negative
speed
nice
23
To differentiate the function y = 2xsinx, we have to use the . . . .
Quotient Rule
Power Rule
Produce Rule
Product Rule
24
Differentiate the function below . . .
y' = -csc2x
y' = sec2x
y' = cotx
y' = -cscxcotx
25
If s(t) is the position function of an object, the second derivative of s(t) is ...
speed
acceleration
2 headaches
velocity
