There is a question in my calculus textbook that asks to find a point on the parabola $y^2 = 2x$ that is closest to point $(1,4)$.
They want us to first use the distance formula, but then proceeded to square it leaving us with $d^2 = (y^2/2 - 1)^2 + (y-4)^2$.
I am following the math up to this point, where I get lost is when the textbook states "You should convince yourself that the minimum of $d^2$ occurs at the same point as the minimum of $d$, but $d^2$ is easier to work with".
I don't understand how that can be true at all, $d$ is a distance between a fixed point and another point on the graph $y^2 = 2x$. $d^2$ must be that distance scaled by itself, how can the minimum be the same then? I've worked out the math for $d$ and $d^2$ and I do get the same point but I don't understand why.