How do you do this problem?

Which points on the graph of y=4-(x^2) are closest to the points (0,2)?

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- November 8th 2009, 12:42 PMPrincessIsraelPlease help me with something my teacher didn't teach us
How do you do this problem?

Which points on the graph of y=4-(x^2) are closest to the points (0,2)? - November 8th 2009, 12:44 PMVonNemo19
- November 8th 2009, 02:18 PMScott H
Welcome to the Math Help Forum! :)

To find the point on closest to , we first do as VonNemo said and use the distance formula to obtain a function of the distance from a point on the curve to as a function of :

We now find the value of for which is a minimum. To do this, we differentiate and find all critical points. As is differentiable everywhere and has no boundary points, the only critical points will be those at which . As approaches infinity in both directions of the -axis, at one of these critical points we must find our minimum.

Hope this helps!