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March 20th, 2017, 04:40 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3  Partial Derivative Application for shortest distance
Find the shortest distance from the point (0, 0, b) to the paraboloid z = x^2 + y^2. D = sqrt(( x  0 )^2 + ( y  0 )^2 + ( x^2 + y^2  b )^2) D = sqrt( x^2 + y^2 + x^4 + 2x^2y^2  2bx^2  2by^2 +b^2 + y^4 ) âˆ‚D/âˆ‚x = 2x + 4x^3 + 4xy^2  4bx = 1 + 2x^2 + 2y^2  2b = 0 âˆ‚D/âˆ‚y = 2y + 4y^3 + 4x^2y  4by = 1 + 2y^2 + 2x^2  2b = 0 2 unknowns but with one equation, I am stuck! Any tips would be much appreciated.... 
March 20th, 2017, 05:47 PM  #2  
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 
Would the following correct? 1  4x^2  2b = 0 4x^2 = 2b  1 x^2 = (2b  1)/4 x = sqrt((2b  1) /4) Quote:
 

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application, derivative, distance, partial, shortest 
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