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Math Problems
Calculus
Euler's method
Let
f
(
x
)
=
2
x
3
+
21
x
2
+
36
x
f(x)=2 x^{3}+21 x^{2}+36 x
f
(
x
)
=
2
x
3
+
21
x
2
+
36
x
.
\newline
What is the absolute maximum value of
f
f
f
over the closed interval
[
−
8
,
0
]
[-8,0]
[
−
8
,
0
]
?
\newline
Choose
1
1
1
answer:
\newline
(A)
32
32
32
\newline
(B)
180
\mathbf{1 8 0}
180
\newline
(C)
108
\mathbf{1 0 8}
108
\newline
(D)
0
0
0
Get tutor help
Let
h
(
x
)
=
−
2
x
3
−
7
h(x)=-2 x^{3}-7
h
(
x
)
=
−
2
x
3
−
7
.
\newline
The absolute maximum value of
h
h
h
over the closed interval
[
−
3
,
2
]
[-3,2]
[
−
3
,
2
]
occurs at what
x
x
x
-value?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
-3
−
3
\newline
(B)
2
2
2
\newline
(C)
1
1
1
\newline
(D)
−
2
-2
−
2
Get tutor help
Let
h
(
x
)
=
x
3
+
6
x
2
+
2
h(x)=x^{3}+6 x^{2}+2
h
(
x
)
=
x
3
+
6
x
2
+
2
.
\newline
What is the absolute minimum value of
h
h
h
over the closed interval
−
6
≤
x
≤
2
-6 \leq x \leq 2
−
6
≤
x
≤
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
34
34
34
\newline
(B)
−
34
-34
−
34
\newline
(C)
2
2
2
\newline
(D)
−
2
-2
−
2
Get tutor help
Let
g
(
x
)
=
2
x
3
−
21
x
2
+
60
x
g(x)=2 x^{3}-21 x^{2}+60 x
g
(
x
)
=
2
x
3
−
21
x
2
+
60
x
.
\newline
What is the absolute maximum value of
g
g
g
over the closed interval
[
0
,
6
]
[0,6]
[
0
,
6
]
?
\newline
Choose
1
1
1
answer:
\newline
(A)
42
42
42
\newline
(B)
25
25
25
\newline
(C)
52
52
52
\newline
(D)
36
36
36
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Let
h
(
x
)
=
x
3
−
6
x
2
+
8
h(x)=x^{3}-6 x^{2}+8
h
(
x
)
=
x
3
−
6
x
2
+
8
.
\newline
The absolute minimum value of
h
h
h
over the closed interval
−
1
≤
x
≤
6
-1 \leq x \leq 6
−
1
≤
x
≤
6
occurs at what
x
x
x
value?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
4
4
4
\newline
(C)
6
6
6
\newline
(D)
−
1
-1
−
1
Get tutor help
Let
g
(
x
)
=
3
x
3
+
8
g(x)=3 x^{3}+8
g
(
x
)
=
3
x
3
+
8
.
\newline
What is the absolute minimum value of
g
g
g
over the closed interval
−
2
≤
x
≤
2
-2 \leq x \leq 2
−
2
≤
x
≤
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
16
-16
−
16
\newline
(B)
16
16
16
\newline
(C)
8
8
8
\newline
(D)
−
8
-8
−
8
Get tutor help
Let
f
(
x
)
=
−
x
3
+
3
x
2
−
6
f(x)=-x^{3}+3 x^{2}-6
f
(
x
)
=
−
x
3
+
3
x
2
−
6
.
\newline
The absolute maximum value of
f
f
f
over the closed interval
[
−
2
,
5
]
[-2,5]
[
−
2
,
5
]
occurs at what
x
x
x
-value?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
5
5
\newline
(B)
0
0
0
\newline
(C)
2
2
2
\newline
(D)
−
2
-2
−
2
Get tutor help
The average cost per meal served at Kiran's restaurant decreases at a rate of
2400
q
2
\frac{2400}{q^{2}}
q
2
2400
dollars per meal served that month (where
q
q
q
is the number of meals served).
\newline
By how many dollars does the average cost per meal decrease between
q
=
300
q=300
q
=
300
and
q
=
360
q=360
q
=
360
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
67
67
67
\newline
(B)
0
0
0
.
81
81
81
\newline
(C)
1
1
1
.
11
11
11
\newline
(D)
1
1
1
.
33
33
33
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Let
f
(
x
)
=
x
3
+
6
x
2
+
6
x
f(x)=x^{3}+6 x^{2}+6 x
f
(
x
)
=
x
3
+
6
x
2
+
6
x
and let
c
c
c
be the number that satisfies the Mean Value Theorem for
f
f
f
on the interval
[
−
6
,
0
]
[-6,0]
[
−
6
,
0
]
.
\newline
What is
c
c
c
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
-5
−
5
\newline
(B)
−
4
-4
−
4
\newline
(C)
−
3
-3
−
3
\newline
(D)
−
1
-1
−
1
Get tutor help
Let
h
(
x
)
=
x
3
−
9
x
2
+
7
x
h(x)=x^{3}-9 x^{2}+7 x
h
(
x
)
=
x
3
−
9
x
2
+
7
x
and let
c
c
c
be the number that satisfies the Mean Value Theorem for
h
h
h
on the interval
−
3
≤
x
≤
6
-3 \leq x \leq 6
−
3
≤
x
≤
6
.
\newline
What is
c
c
c
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
3
3
3
\newline
(D)
4
4
4
Get tutor help
Let
h
(
x
)
=
x
3
−
6
x
2
−
10
x
h(x)=x^{3}-6 x^{2}-10 x
h
(
x
)
=
x
3
−
6
x
2
−
10
x
and let
c
c
c
be the number that satisfies the Mean Value Theorem for
h
h
h
on the interval
[
−
4
,
5
]
[-4,5]
[
−
4
,
5
]
.
\newline
What is
c
c
c
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
-2
−
2
\newline
(B)
−
1
-1
−
1
\newline
(C)
1
1
1
\newline
(D)
3
3
3
Get tutor help
Let
g
(
x
)
=
x
3
+
12
x
2
+
36
x
g(x)=x^{3}+12 x^{2}+36 x
g
(
x
)
=
x
3
+
12
x
2
+
36
x
and let
c
c
c
be the number that satisfies the Mean Value Theorem for
g
g
g
on the interval
−
8
≤
x
≤
−
2
-8 \leq x \leq-2
−
8
≤
x
≤
−
2
.
\newline
What is
c
c
c
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
7
-7
−
7
\newline
(B)
−
6
-6
−
6
\newline
(C)
−
3
-3
−
3
\newline
(D)
−
1
-1
−
1
Get tutor help
Let
f
(
x
)
=
x
3
+
9
x
2
+
13
x
f(x)=x^{3}+9 x^{2}+13 x
f
(
x
)
=
x
3
+
9
x
2
+
13
x
and let
c
c
c
be the number that satisfies the Mean Value Theorem for
f
f
f
on the interval
−
7
≤
x
≤
−
1
-7 \leq x \leq-1
−
7
≤
x
≤
−
1
.
\newline
What is
c
c
c
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
6
-6
−
6
\newline
(B)
−
5
-5
−
5
\newline
(C)
−
3
-3
−
3
\newline
(D)
−
2
-2
−
2
Get tutor help
Let
f
(
x
)
=
x
3
−
6
x
2
+
12
x
f(x)=x^{3}-6 x^{2}+12 x
f
(
x
)
=
x
3
−
6
x
2
+
12
x
and let
c
c
c
be the number that satisfies the Mean Value Theorem for
f
f
f
on the interval
[
0
,
3
]
[0,3]
[
0
,
3
]
.
\newline
What is
c
c
c
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
1
1
\newline
(C)
2
2
2
\newline
(D)
3
3
3
Get tutor help
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