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Mathematics
Mathematics
Problem
Consider the polynomial function
P
(
x
)
=
5
x
7
−
3
x
5
+
6
x
3
−
8
x
2
+
4
x
−
9.
P(x)=5x^{7}-3x^{5}+6x^{3}-8x^{2}+4x-9.
P
(
x
)
=
5
x
7
−
3
x
5
+
6
x
3
−
8
x
2
+
4
x
−
9.
(i) Find
P
′
(
x
)
P'(x)
P
′
(
x
)
. (ii) Calculate
P
′
(
1
)
P'(1)
P
′
(
1
)
and
P
′
(
2
)
P'(2)
P
′
(
2
)
. (iii) Hence determine the rate of change of
P
(
x
)
P(x)
P
(
x
)
at
x
=
1
x=1
x
=
1
and
x
=
2
x=2
x
=
2
.
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