Posted by **Tracy** on Friday, November 17, 2006 at 4:51pm.

Hey there. I have a quick question. Ive done questions like these before so I don't know whats stoping me. Anways the question is this:

Find a point on the graph of

y = x^2

with x>0 that lies closest to (0, 3). What is the x-coordinate of such a point?

So I got 3^2 + y^2 = x^2 and solved for x but after that I'm lost. Normally that's what we did, but our other equations was normally like xy=8 so now I'm kinda lost. Any help would be apperciated. Thanks

The distance d from apoint with coordinates (x,y) to the point (0,3) is given by:

d^2 = x^2 + (y-3)^2

You have to minimize this while satisfying the constraint that he point (x,y) be on te parabola. So the contraint is:

y = x^2

This means that:

d^2 = y + (y-3)^2

You have to minimize this function.

Okay, so would you mind checking this? I've lost so many points already I don't wanna enter any more wrong answers.

If we have d^2 = y + (y-3)^2 then d =(y + (y-3)^2) ^1/2 (aka the root is what im getting at) So then if I take the derivative and then make it equal zero I get y = 3, so then x would equal the root of 3?

Hmm well I guess I went wrong somwheres because I put that it and it says its not right.

Sorry again. I missed something when I did the derivative and while adding something together I forgot something out. So now I have that y=5/2 and x=sqrt5/2

This is correct. Note that you can just differentiate d^2 instead of d. The square of a positive function is minimal (maximal) if and only if the function itself is minimal (maximal).

## Answer This Question

## Related Questions

- URGENT! Last calculus question! - Hey! So, I was wondering if someone could ...
- Calculus - Would you be able to help me with a couple of questions? thanks in ...
- calculus - conic sections question 1: verify that the point (3,2) lies on the ...
- Calculus - Find dy/dx at the point (-3, 1) for the equation x = y^3-9y^2+5. A. -...
- calculus - hey guys, quick question (-8 +- sqrt -20)/-6 what does this equal
- very complicated maths - Hey guys, need some help with a question ive been stuck...
- Reading Analogy - Hey Everyone! I have a quick question! I'm doing this reading ...
- Algebra - Question 1 Solve using the multiplication principle then graph. -15>...
- geography - hi guys , anyone having trouble finding info about broughton airbus...
- geography - hi guys , anyone having trouble finding info about broughton airbus...

More Related Questions