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?

Answer 1

HI!!

Answer 2

probably calculus

Answer 3

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

Answer 4

lol then that is what you can use

Answer 5

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

Answer 6

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

Answer 7

I know I should take a derivative right?

Answer 8

implicitly or otherwise with respect to x?

Answer 9

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

Answer 10

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

Answer 11

Help?