anonymous
  • anonymous
Optimization Problem: Find a point on the line y = 2x+5 that is closest to the origin
Mathematics
schrodinger
  • schrodinger
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Savvy
  • Savvy
distance of origin from a pt. on the line is sqrt.[(x)^2 + (2x+5)^2].................square it since the distance and its square maximise simoultaneously and then differentiate with respect to x and find the minima....the corresponding value of x and y will give you the required point....
anonymous
  • anonymous
Thanks, that is correct sir. Except I'm not sure why you differentiate D^2 instead of D. Will differentiating D give you the same answer? My textbook mentions the same thing, but it doesn't really explain why
Savvy
  • Savvy
yeah differentiating D would also yield the same answer but differentiating a square root is a tedious job so instead we diff. D^2......if D is min. for some value of x, it's square will also be min. at same value of x as compared to the other values....got it..???

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anonymous
  • anonymous
oh okay, that's pretty intuitive i guess

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