Exercises
UF Calculus Set 11
1. Find the equation of the tangent line to the graph of the function
f
(
x
) =
x
2
+ 2
x
at the point
( 1
,
3 )
. Sketch both the graph of
f
(
x
)
and the tangent line on the same axes.
2. Find the equation of the line tangent to the given curve at the given point.
(a)
y
= 3
x

4
;
( 1
,

1 )
(b)
y
= 2
x
2
;
(

1
,
2 )
(c)
y
=
√
x
;
( 1
,
1 )
(d)
y
=
x
3

x
;
( 0
,
0 )
(e)
y
=
√
t

1
;
( 5
,
2 )
(f)
y
= (
x

2)

1
;
( 1
,

1 )
3. Find all points
P
on the parabola
y
=
x
2
such that the tangent line at
P
passes through the
point
( 0
,

4 )
. What if the point were changed to
( 2
,

5 )
?
4. The position functions of two objects,
A
and
B
are sketched below. The horizontal axis is
measured in minutes and the vertical axis in meters. Answer the questions below.
(a) Which object travels a farther distance over the ﬁrst 8 minutes? 12 minutes?
(b) After how many minutes do the objects have the same average velocity to that point?
(c) Which object is traveling faster after 2 minutes? 5 minutes?
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 Spring '08
 ALL
 Calculus, Geometry, Continuous function, Euclidean geometry

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