Question

Maxima and Minima: Find the smallest distance of from a point from x^2 to 10,0.

Answer 1

lagrange?

Answer 2

Round off the the nearest tenths.

Answer 3

I'm still thinking -.-

Answer 4

minimum of:\[\sqrt{(x-10)^2+(x^2-0)^2}\]

Answer 5

I got an answer that looks really wrong.

Answer 6

Anyone got an answer?

Answer 7

patience...

Answer 8

>.<

Answer 9

grad F=<2(x-10),2y>
grad G=<-2x,1>

2(x-10)= -2x lambda
2x-20=-2x lambda

2y= lambda
y-x^2=0

http://www.wolframalpha.com/input/?i=Solve%5B2x-20%3D-2x%20*a%2C%202y%3Da%2C%20y-x%5E2%3D0%5D&t=crmtb01

x=1.61
y=2.60

Answer 10

PaxPolaris is correct; the distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\). Since the function \(f(x)=x^2\) can be expressed as an ordered pair by \((x,x^2)\), and you're given the point \((10,0)\), you can substitute those values instead.\[\]

Answer 11

Thats what I got...

Answer 12

what did you get?

Answer 13

your ans

Answer 14

I used lagrange multiplier ; which is useful for finding min/max while staying on curve/surface

Answer 15

?

Answer 16

I consider this problem solved.

Answer 17

you can just forget the square root get the minimum of the square of the distance