Question

Find the shortest distance between the curve y = 3/x, for x > 0 and the origin??

Answer 1

The distance of a point and the origin is d = sqrt(x^2 + y^2). Minimizing d is the same as minimizing d^2, so let's use that instead. Let

f(x) = d^2
= x^2 + y(x)^2
= x^2 + 9/x^2

Now minimize f. E.g., find the derivative, set it equal to zero, etc.

Answer 2

i did that and got radical(3) and its wrong?

Answer 3

That's right \( x = \sqrt{3} \) and hence \( y = \sqrt{3} \) also.

I.e., the point, p, on the graph of the y = 3/x closest to the origin is
\[ p = (\sqrt{3}, \sqrt{3}) \]

Answer 4

But the question asks what's the distance. So calculate d for that value of (x,y)

Answer 5

Oh okay radical(6)