Brain Teaser  Minimum distance between two curves

01022016, 06:14 PM
Post: #14




RE: Brain Teaser  Minimum distance between two curves
1. The coordinates at f(x) are (x,x^2+1); at g(y) are (y,sqrt(y)). Using a global minimization for the distance, the lowest distance possible is ~0.427592 where x=~0.331695 and y=~0.568071.
2. This x is the (real) root of the equation 4*x^5+6*x^3x^2=1/8 3. More precisely y is ~0.5680712803530178751565860996, but I could not find a single proper closed form for this. Done with Mathematica/WolframAlpha. 

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