1. ## Hyperbola point

1) Find the point on the hyperbola xy=8 closest to (3,0).

I honestly, have no idea what to do. I seriously do not remember discussing anything like this in class, nor having any previous problems in homework. If anyone can give me a start or walkthrough, that would be fantastic!

hmm alright.

Ive gotten too $\displaystyle squareroot(x^2 - 6x + 9 +64/x^2)$

but am not sure how to get from there, to the minimum

2. Originally Posted by karisrou
hmm alright.

Ive gotten too $\displaystyle squareroot(x^2 - 6x + 9 +64/x^2)$

but am not sure how to get from there, to the minimum
Now differentiate (use the chain rule). Then equate the derivative to zero. After a bit of algebra you have

$\displaystyle x^4 - 3x^3 - 64 = 0$.

Now solve for x.

I think you'll find that x = 4 gives the minimum value ....

3. When you use the chain rule, wouldnt you have to put 2 times the radical below the derivative of the contents of the radical?

4. Originally Posted by karisrou
When you use the chain rule, wouldnt you have to put 2 times the radical below the derivative of the contents of the radical?
Yes. Have you differentiated, equated to zero and done a bit of algebra ....? The you will get the quartic I posted.

Note that if $\displaystyle \frac{A}{B} = 0$ then $\displaystyle A = 0 \, ....$