Optimization - Max Vertical Distance

In this video I showed how to optimize the vertical distance between two functions

[yuanxiangli-kv]

Thank you sooo much for explaining the reason behind each steps. Explained very clearly.

[pramodkchintamani]

Interesting and very helpful. Thank u sir

[mikefochtman]

Intuitively, looking at the graph, the maximum will be when the slopes of the two lines are equal. To one side, one line is rising faster than the other and the distance is either growing or shrinking. So the slope of y=x+42 is 1 all the time, where is the slope of y=x^2 equal to 1? Obviously the f(y)` = 2x, so 1= 2x => x= 1/2. Kind of a 'cheat', but this problem lends itself to this way of looking at it.

[lesliesusil]

Sir l have learned that the distance between x1y1 and x2y2 is [(x2-x1)^2 +(y2-y1)^2]^1/2 .but your method is different.why?

[suyunbek]

woah man thats tough, even your subscribers aren't subscribed to you *sad_emoji*