Find the point on the curve y=√(4x) that is closest the the point (3,0)

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Homework Statement


Find the point on the curve y=√(4x) that is closest the the point (3,0)


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The Attempt at a Solution


I don't even know where to start.
 
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What's the distance between (x,sqrt(4x)) and (3,0)?
 
It wasnt given. The only thing given was the point, and the equation.
 
mg2 said:
It wasnt given. The only thing given was the point, and the equation.

No, no. In general, what's the distance between two points (a,b) and (c,d)? Use a general distance formula. You don't have to be given the formula.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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