Find the point on the hyperbola xy=10 closest to the point (3,0). Is there a way to do this without looking at a graph?

Question

Find the point on the hyperbola xy=10 closest to the point (3,0).  Is there a way to do this without looking at a graph?

misty1212 · Answer

HI!!

misty1212 · Answer

probably calculus

daniel.ohearn1 · Answer

I hope so, it's for my Calculus 1A class..

misty1212 · Answer

lol then that is what you can use

misty1212 · Answer

a point on the graph will look like $(x,\frac{10}{x})$

misty1212 · Answer

and the square of the distance between that point and $(3,0)$ will be $$\large (x-3)^2+\left(\frac{10}{x}\right)^2$$
minimize that in the usual calc way

daniel.ohearn1 · Answer

I know I should take a derivative right?

daniel.ohearn1 · Answer

implicitly or otherwise with respect to x?

daniel.ohearn1 · Answer

If I take a derivative and solve it for zero I get 2x^4 - 6x^3 = 0 .... 
hmm..

daniel.ohearn1 · Answer

I got x=(1/3)^(5/4) but that can't be right.. I'm not sure how to do this atm..

daniel.ohearn1 · Answer

Help?