
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 20th, 2017, 05:40 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, 06:47 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:
 

Tags 
application, derivative, distance, partial, shortest 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Partial Derivative Application about optimization of dimension  zollen  Calculus  5  March 14th, 2017 05:21 AM 
Shortest distance triangle  bracke  Algebra  3  May 10th, 2012 10:44 AM 
shortest distance  mikeportnoy  Algebra  5  May 16th, 2010 03:56 PM 
shortest distance between line and curve  gaziks52  Algebra  4  April 11th, 2009 12:58 PM 
shortest distance  arun  Algebra  6  March 4th, 2007 10:01 AM 