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Mathematics
Problem
For
f
(
x
)
=
x
5
f(x)=x^{5}
f
(
x
)
=
x
5
, the difference quotient is
f
(
x
+
h
)
−
f
(
x
)
h
\displaystyle \frac{f(x+h)-f(x)}{h}
h
f
(
x
+
h
)
−
f
(
x
)
. After factorising
h
h
h
from the numerator, which expression remains in the numerator? a)
5
x
4
+
5
x
3
h
+
5
x
2
h
2
+
5
x
h
3
+
h
4
5x^{4}+5x^{3}h+5x^{2}h^{2}+5xh^{3}+h^{4}
5
x
4
+
5
x
3
h
+
5
x
2
h
2
+
5
x
h
3
+
h
4
b)
5
x
4
+
10
x
3
h
+
10
x
2
h
2
+
h
5
5x^{4}+10x^{3}h+10x^{2}h^{2}+h^{5}
5
x
4
+
10
x
3
h
+
10
x
2
h
2
+
h
5
c)
5
x
4
+
10
x
3
h
+
10
x
2
h
2
+
5
x
h
3
+
h
4
5x^{4}+10x^{3}h+10x^{2}h^{2}+5xh^{3}+h^{4}
5
x
4
+
10
x
3
h
+
10
x
2
h
2
+
5
x
h
3
+
h
4
d)
5
x
4
+
10
x
3
h
+
10
x
2
h
2
+
5
x
h
3
5x^{4}+10x^{3}h+10x^{2}h^{2}+5xh^{3}
5
x
4
+
10
x
3
h
+
10
x
2
h
2
+
5
x
h
3
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