Point on the curve closest to (18,1)

Faraz Ahmed
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Question:
Question: Find the point on the curve y=x^2 +1 that is closest to the point (18,1).

Please see the image and that’s where I’m stucked- after taking the first derivate. Please solve it further step by step completely. It’d mean a lot.
 

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We won't do your homework for you here - it is your homework.

Which value does the derivative have to reach at the minimum?

Afterwards you'll have to try different values for u to find the solution (there is a formula but that is more complicated than testing different values).
 
Faraz Ahmed said:
Question:
Question: Find the point on the curve y=x^2 +1 that is closest to the point (18,1).

Please see the image and that’s where I’m stucked- after taking the first derivate. Please solve it further step by step completely. It’d mean a lot.

It is against PF rules for us to do complete solutions; we are allowed to offer hints, but not more.

Here is a hint: minimizing the squared-distance will give the same solution as minimizing the distance itself----can you see why? --- and the squared-distance problem is easier.
 

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