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Duplicate of MCV4U Final Exam Review
Duplicate of MCV4U Final Exam Review
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MCV4U Final Exam review #calculus #derivatives #vectors #limits #rateofchange
Flashcards
31 cards
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Questions
31
Answers
1
What is the Product Rule ?
(f ')(g) + (g')(f)
none
(f )(g) + (g')(f')
(f ')(g) - (g')(f)
2
Given the function f(x) = e
-x
, the derivative f'(x) = ?
1
-e-x
e-x
xex
3
What type of asymptote is found when you find the limit f(x) as x-----> ±∞
vertical asymptotes
oblique asymptotes
slant asymptotes
horizontal asymptotes
4
Given the function f(x) = 4x
5
, the derivative of the function f'(x) = ?
5x4
20x4
80x3
x2
5
Given the function h(x) = -17 , the derivative of the function h'(x) = ?
17
-17
-17x-1
0
6
The process of setting the derivative of a function equal to zero and solving it is called ?
optimization
dependence
tangent
first principles
7
The process of finding a derivative by using limits and f(x+h)-f(x) is called ?
first principles
rationalizing
factoring
optimization
8
The limit of the following function, as x ---> 3, is ______________
3
4
dne (does not exist)
1
9
Given the function f(x) = ln(4x)
, the derivative f'(x) = ?
4x
1/x
1/4
ln e
10
What is the value of ln e ?
none of these
e
cos x
0
11
What is the derivative of the function f(x) = (2x
3
+ 1)
5
?
5(2x3 +1)4
5(6x2 )4
2x15 + 1
5(2x3 +1)4 (6x2)
12
The limit of the following function ?
7
5
undefined
0
13
If the displacement function is given as s(t) = t
4
, then the velocity function is ?
v(t) = 4t3
v(t) = 12t2
v(t) = 4t3 + t2
v(t) = 4t2
14
What is the Quotient Rule?
{(f ')(g) + (f)(g')} / g2
{(f )(g') - (f ')(g)} / g2
{(f ')(g) - (f)(g')} / g2
(f ')(g) + (f)(g')
15
Given the function f(x) = ln x
, the derivative f'(x) = ?
ex
x2
x-2
1/x
16
If the displacement function is given as s(t) = t
4
, then the acceleration function is ?
a(t) = 4t3
a(t) = 4t3 + t2
a(t) = 12t2
a(t) = 4t2
17
Given the function f(x) = -3x
3
+ x
2
+ 1, the derivative of the function f'(x) = ?
-9x2 + 2x
-9x2 + 2
-9x2 + 2x + 1
-9x2
18
Given the function f(x) = x
100
+ 100x
-2
, the derivative of the function f'(x) = ?
100x99 +100
100x99 - 200x-3
100x99 - 200x-1
100x99 + 200x-3
19
The rate of change of a function is the _________________ ?
slope
reciprocal
absolute value
inverse
20
Point A is a _________________?
local maximum
global maximum
global minimum
local minimum
21
Given the function f(x) = e
x
, the derivative f'(x) = ?
1
1/x
0
f'(x) = ex
22
log
3
x + 2log
3
y - log
3
z =
log3(xy/2z)
any of these
log3(x2y/z)
log3(xy2/z)
23
The ______________ is when a tangent is used to find the rate of change (at only one point).
y"
secant
average rate of change
instantaneous rate of change
24
In the interval x ϵ [0,7], Point E and F are _________________?
global minimums
global maximums
local maximums
local minimums
25
What is the Chain Rule?
a way to determine the derivative of a composite function
f'(g(x) . g'(x)
dy/du . du/dx
all of these
26
Given the function g(x) = ∛x , the derivative of the function g'(x) = ?
x-1/3
2x-1/3 / 3
x2/3
x-2/3 / 3
27
Given the function f(x) = 3
x
, the derivative f'(x) = ?
x . (3x-1)
3ex
ln 3 . (3x)
x3
28
Point D is a _________________?
local maximum
global maximum
local minimum
global minimum
29
Given the function f(x) = x
4/5
, the derivative of the function f'(x) = ?
4x-1/5 / 5
5x-1/5 / 4
5x-4/5 / 4
4x-3/5 / 5
30
Point B is a _________________?
global maximum
global minimum
local minimum
local maximum
31
Another notation to represent derivative is ?
df
dx/dy
dy/dx
y"
