Point on the curve closest to (18,1)

In summary, the conversation is about finding the point on the curve y=x^2+1 that is closest to the point (18,1). The person asking for help is stuck after taking the first derivative and is asking for further assistance. The other person provides a hint about minimizing the squared-distance to find the solution.
  • #1
Faraz Ahmed
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Member warned that the homework template must be used
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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  • #2
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).
 
  • #3
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.
 

1. What is the significance of the point (18,1) in relation to the curve?

The point (18,1) serves as a specific coordinate on the curve, indicating the position at which the distance to the nearest point on the curve is being measured.

2. How is the point on the curve closest to (18,1) determined?

The point on the curve closest to (18,1) is determined by finding the point on the curve that has the shortest distance to the given point. This can be calculated using mathematical algorithms and techniques such as calculus.

3. Can the point on the curve closest to (18,1) change?

Yes, the point on the curve closest to (18,1) can change depending on the shape and position of the curve. If the curve is altered or shifted, the point closest to (18,1) may also change.

4. What factors can affect the location of the point on the curve closest to (18,1)?

The location of the point on the curve closest to (18,1) can be affected by the shape, position, and orientation of the curve, as well as the position of the given point (18,1).

5. How is the point on the curve closest to (18,1) used in real-world applications?

The concept of finding the point on the curve closest to a given point has various applications in fields such as engineering, physics, and computer graphics. For example, it can be used to optimize the design of structures or to accurately position objects in 3D space.

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