What did i do wrong?

[Panceta]

I'm looking for q.

 

[Deleted member 4993]

I'm looking for q.
View attachment 14705

Your attachment is dark (unreadable) in the 3rd. quadrant.

Please print the whole question as it was given to you.

 

[pka]

I'm looking for q.
View attachment 14705

Please if you want our help then follow the posting guidelines.
You post the exact wording of the problem. You tell us where you are having trouble,
Please don't ask to us to look at a jumble of scratching to figure all of that out.

 

[Panceta]

Oh, my bad.

The question is: ‘if u have a point P(5,1) and a point Q(x,y) that’s situated on the graph y = x^2/2 than what are the coordinates of Q so that the distance |PQ| is as small as possible?’

And the third quadrant:

 

[Steven G]

The question is: ‘if you have a point P(5,1) and a point Q(x,y) that’s situated on the graph y = x^2/2 than what are the coordinates of Q so that the distance |PQ| is as small as possible?’

I am tired of trying to follow this post as I can not read your images.
This is a standard Calculus 1 problem.

Let Q=(x,y) be on the curve y=x^2/2
Then the distance between Q and P is D= [(x-5)^2 + (y-1)^2]^.5 subject to y=x^2/2

So you want to minimize D = [(x-5)^2 + (x^2/2-1)^2]^.5

Can you continue from here?

 

[HallsofIvy]

Since this is a quadratic you don't even need Calculus to find the minimum: complete the square!

(And it certainly doesn't have anything to do with "differential equations".)