Question 9 - Week 8 Practice | Prasnya
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Quiz 2
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Week 8
Question 9
00:00
Est. 3 min
Marks:
+4.00
0.00
Let
f
f
be a polynomial of degree
5
5
, given by
f
(
x
)
=
a
5
x
5
+
a
4
x
4
+
a
3
x
3
+
a
2
x
2
+
a
1
x
+
a
0
f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0
. Let
f
′
(
b
)
f'(b)
denote the derivative of
f
f
at
x
=
b
x=b
. Choose the set of correct options.
Multiple correct
Medium Difficulty
01 December 2024
A
a
1
=
f
′
(
0
)
a_1=f'(0)
.
B
5
a
5
+
3
a
3
=
1
2
{
f
′
(
1
)
+
f
′
(
−
1
)
−
2
f
′
(
0
)
}
5a_5+3a_3=\frac{1}{2}\{f'(1)+f'(-1)-2f'(0)\}
.
C
4
a
4
+
2
a
2
=
1
2
{
f
′
(
1
)
−
f
′
(
−
1
)
}
4a_4+2a_2=\frac{1}{2}\{f'(1)-f'(-1)\}
.
D
a
1
=
f
′
(
1
)
a_1=f'(1)
.
