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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
2
(
x
−
1
)
(
x
+
3
)
(
x
2
+
1
)
f(x)=2(x-1)(x+3)(x^{2}+1)
f
(
x
)
=
2
(
x
−
1
)
(
x
+
3
)
(
x
2
+
1
)
. (a) Write
f
(
x
)
f(x)
f
(
x
)
in expanded polynomial form. (b) Find
f
′
(
x
)
f'(x)
f
′
(
x
)
. (c) Evaluate
f
′
(
1
)
f'(1)
f
′
(
1
)
and interpret its meaning in terms of the slope of the tangent line to the graph of
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
at
x
=
1
x=1
x
=
1
.
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