# Minimum d occurs at minimum d^2

1. Jan 18, 2016

### brycenrg

1. The problem statement, all variables and given/known data
Find the point on the parabola y^2 = 2x that is closest to the point (1,4)

2. Relevant equations
d = ((x-1)^2 + (y-4)^2)^1/2
x=y^2/2
3. The attempt at a solution
My attempt involves subbing in x in the d equation and differentiating it. I cant get the same answer as the book because they differentiate d^2 = not d = to make it easier to solve.
They state "you should convince yourself the minimum of d occurs at the same point as the minimum of d^2, but d^2 is easier to work with"

How do i know it occurs at the same point?

Last edited by a moderator: Jan 18, 2016
2. Jan 18, 2016

### PeroK

Try to find positive $d_1 < d_2$ with $d_1^2 > d_2^2$

3. Jan 18, 2016

### LCKurtz

If $0<a<b$ then $a\cdot a < a \cdot b < b\cdot b$.