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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Solve Exercise 55 when |CD| = 2 cm.

To determine

To find: The position of the point P so that the sum |PA|+|PB|+|PC| is minimized.

Explanation

Given:

The given lengths are |CD|=2 , |BD|=|AD|=4 and CD is perpendicular to AB

Calculation:

Draw the figure showing the arrangement given as shown below in Figure 1.

Note that CD is a perpendicular to AB .

Let PD=x where 0x2

To maximize the distance |PA|+|PB|+|PC| .

Use Pythagoras theorem and determine |PA|=|PB|=16+x2 .

Consider,

f(x)=|PA|+|PB|+|PC|=216+x2+(2x)

Differentiate f with respect to x,

f(x)=2x16+x21=2x16+x216+x2

Equate first derivative to 0

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