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# distance problem (with differentiation) watch

1. Hello!

I've been working on this math problem for some time now, but I can't get my answer to match that of my professor. I don't know if it is because I am doing something wrong, or if the solution he gave us is wrong.

Bear with me!

"Find the point on the line 3x+4y=1 that is closest to the origin."

So, what I did is I use the formula d=x^2+y^2. I then solved for y.

y=(1-3x)/4

So far so good, both my work and my professor's work is the same. Next, I plug this value into my formula.

d=x^2 + {(1-3x)/4}^2

This is also what he did, but the next step is where we differed. We both differentiated, but I got d'(x)=2x -(3/8)(1-3x), whereas he got d'(x)=2x - (3/16)(1-3x). My feelings are that he forgot to drop down the 2 when differentiating. Is this what happened, or am I missing something crucial?

3. (Original post by Rocious)
thank you

An easy way to check the final answer is to note that

Spoiler:
Show
the ray between the closest point and the origin is going to be perpendicular to the line. (Draw to convince yourself.) So in other words, the closest point is the intersection between and .

This is .

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