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1
2005 Calculus #1: Parallel Tangent Lines
2005 Calculus #1: Parallel Tangent Lines
Source:
April 29, 2013
calculus
analytic geometry
graphing lines
slope
Problem Statement
Let
f
(
x
)
=
x
3
+
a
x
+
b
f(x) = x^3 + ax + b
f
(
x
)
=
x
3
+
a
x
+
b
, with
a
≠
b
a \ne b
a
=
b
, and suppose the tangent lines to the graph of
f
f
f
at
x
=
a
x=a
x
=
a
and
x
=
b
x=b
x
=
b
are parallel. Find
f
(
1
)
f(1)
f
(
1
)
.
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