DSC1520 ASSIGNMENT 2 SEMESTER 1 2025 Determine the intervals along which the following function increases or decreases: a. decreases over and , while increases over b. increases over and , while decreases over c. decreases over , while increases o

2/28/25, 1:03 PM Assessment 2




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QUIZ




Question 1

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Evaluate

4
d x − x
[ ]
−
dx √x


.




−−
a. 1
−
7
√x5
2√ x 2



− −−
b. 1
√x −
7
√x5
2 2


− 5 −−
c. 1
√x −
7
√x2
2 2


− −−
d. 2
√x −
7
√x5
3 2



e. None of the given options is correct.

Clear my choice




Question 2

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Find the derivative of the function

1 4 2
f (x) = x − 3x
2




a. 2x
3
− 6x


b. 1
x
3
− 6x
2


1
c. x
4
− 6x
2



d. x
3
− 6x


e. None of the given options is correct.

Clear my choice




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,2/28/25, 1:03 PM Assessment 2

Question 3

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Differentiate

3 2
y = (2x − 4) (x + 1) .




a. 10x
4
+ 6x
2
− 8x


b. 10x
4
− 6x
2
+ 8x


c. 5x
4
+ 3x
2
+ 4x


d. 2
x
6
+
2
x
4
− 2x
3
− 4x
5 3



e. None of the given options is correct.

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Question 4

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Differentiate the function



3 2x
P (x) = x e



2 2x
a. x e (2x + 3)

2x
b. e (2x + 3)


c. x e
5 2x
(x
3
+ 3x )
2




d. 5x e
5 4x




e. None of the given options is correct.

Clear my choice




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,2/28/25, 1:03 PM Assessment 2

Question 5

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Find the derivative




x
y = 20 + ln( ).
−−−−−
√x + 10




a. x+10

2x(x+10)


3x+10
b.
2x(x+5)


2x+9
c.
2(x+5)


1
d.
2(x+5)



e. None of the given options is correct.

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Question 6

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Find the derivative

d 2
(40 + 40 ln Q) .
dQ




3 200
a. (1 + ln Q)
Q



b. 80 (1 +
1
)
Q




c. 80(1 + ln Q)

1 600
d. (1 + ln Q)
Q



e. None of the given options is correct.

Clear my choice




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, 2/28/25, 1:03 PM Assessment 2

Question 7

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Determine the derivative of the function G(t) given by

−−−−−−
3 2
−−−−
G(t) = √t + 9t + 16 .




2

a. 3t +18t

3 2
2√t +9t +16


2

b. 3t +18t

3 2
√t +9t +16


−−−−−−−−− −
c. (3t
2
+ 18t)2√t 3 + 9t 2 + 16

1

d. 1
(t
3
+ 9t
2 −
+ 16) 2
2



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Question 8

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Find the second derivative of the following function:

12 11
−−−−−−−
12
−
11 5
H (x) = (x + 3x )(√x + 3x ) + 13x .




a. 3
1
3
(12x
11
+33x
10
)(12x
11 10
+33x )
′′ 10 9 12 11 2 3
H (x) = (132x + 330x )(x + 3x ) + + 260x .
2 4 √x 12 11
+3x



b. 3
1
3
(12x
11
+33x
10
)(12x
11 10
+33x )
′′ 10 9 12 11 2
H (x) = (132x + 330x )(x + 3x ) + .
2 4 √x12 +3x11




c. 1
(12x
11
+33x
10
)(12x
11 10
+33x )
′′ 3 10 9 12 11 3
H (x) = (132x + 330x )(x + 3x ) 2
− .
2 4 √x 12 11
+3x



d. 3
1
3
(12x
11
+33x
10
)(12x
11 10
+33x )
′′ 10 9 12 11 2 3
H (x) = (132x + 330x )(x + 3x ) − + 260x .
2 4 √x 12 11
+3x




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Question 9

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Determine the intervals along which the following function increases or decreases:

3 2
Q(p) = −p + 9p − 24p + 26.




a. Q(p) decreases over (−∞; 2) and (4; ∞), while increases over (2; 4)

b. Q(p) increases over (−∞; 2) and (4; ∞), while decreases over (2; 4)

c. Q(p) decreases over (−∞; 2) , while increases over (2; 4) and (4; ∞)

d. Q(p) increases over (−∞; 2) , while decreases over (2; 4) and (4; ∞)

Clear my choice




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