BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 43RE
To determine

To find:

The sum |PA|+|PB|+|PC| is a minimum.

Expert Solution

Answer to Problem 43RE

  PD2.31, PA||CD

Explanation of Solution

Given:

  PA=PB=4secθ

  PC=CDPDPC=54tanθ

Concept used:

Triangle ABC with altitude CD

  PC=CDPD

Calculation:

Triangle ABC with altitude CD

Let θ=PAD

  PA=PB=4secθ.......................(1)

  PC=CDPDPC=54tanθ

Differentiating equation (1)

  dSdθ=8.secθ.tanθ4sec2θdSdθ=08.secθ.tanθ4sec2θ=04.secθ(2tanθsecθ)=0

  secθ02tanθ=secθ2sinθcosθ=1cosθcosθ02sinθ=1sinθ=12

Therefore

  θ=π6=300

  P must be placed so that

  PD=4.tan300PD=4.13PD43PD2.31

If cosθ=0

Then θ=900

And PA||CD

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!