2 Optimization problem need help

Mar 2010
33
1
Hello I need step by step all way to get the answer.

1) Find the closest distance of the point (3,1) to the curve xy=8.

2) Find the farthest distance of the point (3,0) to the curve xy=8.
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
Hello I need step by step all way to get the answer.

1) Find the closest distance of the point (3,1) to the curve xy=8.

2) Find the farthest distance of the point (3,0) to the curve xy=8.
1) Let the point on the curve that gives closest distance have coordinates (a, 8/a).

Then \(\displaystyle D^2 = (a - 3)^2 + \left( \frac{8}{a} - 1\right)^2 = .....\)

Now use calculus in the usual way to maximise \(\displaystyle D^2\).


2) is done in a similar way.
 
Mar 2010
33
1
so it doesnt matter if it says closest or farthest distance i would do it the same way to get the answer? what is the step after i maximize?
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
so it doesnt matter if it says closest or farthest distance i would do it the same way to get the answer? what is the step after i maximize?
Have you been taught how to solve an optimisation problem?

You find the stationary points and then check the nature of these stationary points. If you want to maximise then you keep the solution that is a maximum. If you want to minimise then you keep the solution that is a minimum.
 
Mar 2010
33
1
i have just learned it but don't understand too well and i'm allergic to word problems. (Cool)
 
Mar 2010
33
1
would someone be kind enough to solve #1 with all steps listed and explain? im really lost with optimization.
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
would someone be kind enough to solve #1 with all steps listed and explain? im really lost with optimization.
I have set it up for you! All that is essentially left is to find the coordinates of the maximum turning point of D^2. Surely you can do this? If not, you need to go back to your classnotes and textbook and thoroughly review the material that this topic is based on. To find the derivative, I suggest you apply some basic algebra and expand the expression I gave you. Then differentiate it term-by-term.

If you want more help, show some effort. We are not going to just hand you a step-by-step by solution.