Project 22
MAC 2311
1.
Sketch the graph of the function
f
(
x
) =
√
x
on the interval
[ 0
,
6 ]
. Note that
√
6
≈
2
.
5
.
Shade the region between the
x
axis and the curve on your interval. Assume that the axes
measure distance in tens of miles (thus, for example, the distance from the origin to
( 1
,
0 )
is
10
miles).
Suppose the shaded region is a lake and the lakeside towns of Barsad and Cly are located at
the points
( 1
,
1 )
and
( 4
,
2 )
respectively. Draw them on the graph as well.
The towns agree to share the cost of building a straight road between them that is TANGENT
TO the lake. Of course, this means that the road will pass each town to its north. To be fair
to all citizens, the towns want to construct the road so that it has the same perpendicular
distance to each town. Draw (as best as you can) the road on your graph so that each town is
the same perpendicular distance from the road.
What is the relationship between the slope of the road in the
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 Spring '08
 ALL
 Calculus, Road

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