You do NOT need a square root. The derivative of is 2uu' which is 0 only if u= 0 (which cannot happen here, the curve does not go through the point) or if u'= 0 which is what you want.
Hi I'm a bit stuck in this question.
Consider the problem of finding the point on the curve y = x^3/2 that is closest to the point (1, 0).
Model this problem as a non-linear program (NLP) with a single equality constraint.
min (x-1)^2 + y^2
subject to y = x^(3/2)
or would I need... a squareroot on my objective function?