Unformatted text preview: d ﬁnd 3(2 − x)1/3 − x(2 − x)−2/3 ≤ 0 on 2 , 2 ∪ (2, ∞). To
1/3 and g (x) = x(2 − x)−2/3 (the thicker curve).
check this graphically, we set f (x) = 3(2 − x)
3
We conﬁrm that the graphs intersect at x = 2 and the graph of f is below the graph of g for
3
x ≥ 2 , with the exception of x = 2 where it appears the graph of g has a vertical asymptote. (+) 0 (−)
3
2 (−)
2
y = f (x) and y = g (x) One application of algebraic functions was given in Example 1.7.6 in Section 1.1. Our last example
is a more sophisticated application of distance.
Example 5.3.3. Carl wishes to get high speed internet service installed in his remote Sasquatch
observation post located 30 miles from Route 117. The nearest junction box is located 50 miles
downroad from the post, as indicated in the diagram below. Suppose it costs $15 per mile to run
cable along the road and $20 per mile to run cable oﬀ of the road. 320 Further Topics in Functions
Outpost 30 miles z y x Junction Box Route 117
50 miles 1. Express the to...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details