Question

Optimization Problem:
Find a point on the line y = 2x+5 that is closest to the origin

Answer 1

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....

Answer 2

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

Answer 3

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..???

Answer 4

oh okay, that's pretty intuitive i guess