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Derivatives Review
Derivatives Review
23 terms
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StudBud Administration
Calculus -- Derivatives #calculus
Flashcards
23 cards
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Questions
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Answers
1
Differentiate the function below . . .
y' = 7
y' = cosx - sinx
y' = tanx + cotx
y' = sinx + cosx
2
Differentiate the function below . . .
y' = sec2x
y' = secxtanx
y' = -cos2x
y' = cscxcotx
3
If s(t) is the position function of an object, if the object is speeding up, we need to know if
position and velocity have the same signs
velocity and acceleration have different signs
speed is positive
velocity and acceleration have the same signs
4
If s(t) is the position function of an object, the first derivative of s(t) is ...
acceleration
velocity
a headache
speed
5
To differentiate the function y = 2xsinx, we have to use the . . . .
Power Rule
Product Rule
Produce Rule
Quotient Rule
6
The absolute value of velocity is . . . .
nice
negative
speed
acceleration
7
The graph of the derivative of the function below would look like . . . .
a non-horizontal line
a parabola
a cubic function
a horizontal line
8
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) ≠ f(0)
limx→0- f (x) ≠ limx→0+ f (x)
9
Differentiate the function below . . .
y' = -csc2x
y' = cscxcotx
y' = -sinx
y' = -cot2x
10
If s(t) is the position function of an object, a particle is resting when...
time is zero
velocity is zero
acceleration is zero
position is zero
11
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) ≠ f(0)
limx→0- f(x) ≠ limx→0+ f(x)
12
If s(t) is the position function of an object, the second derivative of s(t) is ...
2 headaches
acceleration
velocity
speed
13
Differentiate the function below . . .
y' = -3x3
y' = -6x
y' = -3
y' = -6x2
14
The Quotient Rule: "derivative top x bottom minus top x derivative bottom over ______ squared."
nothing
top
x
bottom
15
True or False: A function can be differentiable but not continuous at a point.
False
True
16
Differentiate the function below . . .
y' = sec2x
y' = secxtanx
y' = cotx
y' = -csc2x
17
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)
18
To find a horizontal tangent to a function f, take the derivative of f and . . .
run
set equal to 0
simplify
set equal to 1
19
This is the . . . .
Alternate Definition of the Derivative
Quotient Rule
Definition of the Derivative
Power Rule
20
The graph of the derivative of a function f(x) describes the _____ of f(x).
asymptotes
life
symmetry
slope
21
Differentiate the function below . . . .
y' = 4x5
y' = 5x
y' = 5x4
y' = x4
22
Differentiate the function below . . .
y' = cotx
y' = -csc2x
y' = sec2x
y' = -cscxcotx
23
True or False: A function can be continuous but not differentiable at a point.
True
False
