Point on the curve closest to (18,1)

Faraz Ahmed
Messages
1
Reaction score
0
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.
 

Attachments

  • 7C125008-7A3D-4CF4-815B-590B8ACA114B.jpeg
    7C125008-7A3D-4CF4-815B-590B8ACA114B.jpeg
    56.1 KB · Views: 613
Physics news on Phys.org
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.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Find Coordinates of Closest Point on y=sqrt(x) to (4,0)
Replies
3
Views
1K
Lagrange multipliers understanding
Replies
8
Views
2K
Closest line from a point to a curve in R^2
Replies
12
Views
2K
Why can't a critical point of a system of DEs be complex?
Replies
27
Views
2K
Calculate this Integral around the Circular Path using Green's Theorem
Replies
3
Views
2K
Simmons 7.10 & 7.11: Find Curves Intersecting at Angle pi/4
Replies
1
Views
2K
Write the tangent lines to the curve
Replies
1
Views
1K
Finding closest point from a parabola to a plane
Replies
3
Views
3K
Finding integral curves of a vector field
Replies
3
Views
2K
Understanding Wronskian of solutions to homoeneous 2nd order linear DE
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top