Page 153 - Calculus Workbook For Dummies

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Chapter 8: Using Differentiation to Solve Practical Problems

17. Find all lines through (0, 1) normal to the 18. An ill-prepared adventurer has run out of
4
curve y = x . The results may surprise you. water on a hot sunny day in the desert.
Before you begin solving this, graph y = x 4 He’s 30 miles due north and 7 miles due
and put the cursor at (0, 1). Now guess east of his camp. His map shows a winding
where normal lines will be and whether river — that by some odd coincidence
they represent shortest paths or longest happens to flow according to the function
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paths from (0, 1) to y = x . Note: Do y = 10 sin x + 10 cos x + x (where his
ZoomSqr to get the distances on the graph 10 5
to appear in their proper proportion. camp lies at the origin). See the following
figure. What point along the river is closest
Solve It to him? He figures that he and his camel can
just barely make it another 15 miles or so.
y
50

40
30

20
10
Camp
10 20 30 40 50 x

Solve It