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Mathematics
Mathematics
Problem
The Maclaurin polynomial of a function
f
f
f
is
P
4
(
x
)
=
5
+
4
x
+
b
x
2
+
c
6
x
3
+
d
24
x
4
.
P_4(x)=5+4x+bx^{2}+\frac{c}{6}x^{3}+\frac{d}{24}x^{4}.
P
4
(
x
)
=
5
+
4
x
+
b
x
2
+
6
c
x
3
+
24
d
x
4
.
The derivatives of
f
f
f
at
x
=
0
x=0
x
=
0
satisfy
f
′
′
(
0
)
=
f
′
(
0
)
+
2
f''(0)=f'(0)+2
f
′′
(
0
)
=
f
′
(
0
)
+
2
and
f
′
′
′
(
0
)
=
3
f
′
′
(
0
)
−
6
f'''(0)=3f''(0)-6
f
′′′
(
0
)
=
3
f
′′
(
0
)
−
6
. What is the value of
c
c
c
? a)
6
6
6
b)
24
24
24
c)
12
12
12
d)
18
18
18
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