Question

What is the shortest distance from (0,0) to y=-4/x ?

Answer 1

Hi there ! welcome to openstudy !

Answer 2

About your question first convert the line into standard form

Answer 3

so how would I do that?

Answer 4

would someone help me please?

Answer 5

use the formula to get distance of two points A(x1,y1) and B(x2,y2)
d = sqrt{(x1-x2)^2 + (y1-y2)^2}

Answer 6

let A=(0,0) and B(x, -4/x)
apply that points to formula above

Answer 7

then derive, just take the first derivative and make equal 0
solve for x

Answer 8

why do you have to let A=(0,0) and B=(x, -4/x) ?

Answer 9

that's ur point given, right

Answer 10

ur question : What is the shortest distance from (0,0) to y=-4/x
we need 2 point to calculate the distance of both

Answer 11

okay I think I understand why. So everytime I encounter a problem like this, do I just let the point be A and the other be the y-value of another point?

Answer 12

yeah, that's i mean :)

Answer 13

okay thank you.

So I just have to simply substitute them in the equation that you mentioned above and solve, right?

Answer 14

yup, have u learned derivative before ?

Answer 15

yes, I am in Calculus II.

Answer 16

okay, i sure u can solve this

Answer 17

take the derivative of the distance, right?

Answer 18

yes

Answer 19

\[d=\sqrt{x^2{+}\frac{ 16 }{ x^2{} }}\]
Is that correct?

Answer 20

yup, now derive d/dx (d')

Answer 21

so \[x^4=32\]

Answer 22

hint :derivative of sqrt(f(x)) is f ' /2sqrt(f(x))

Answer 23

and x=\[2\sqrt{2}\]

Answer 24

hmmm .. i got diferent like yours

Answer 25

i got an equation x^4 = 16, and finally get x= +-2

Answer 26

I just double checked my work and I don't think I made a mistake...