Question

PLEASE HELP ME. THIS IS THE THIRD THREAD AND IVE BEEN AT IT FOR MORE THAN 2 HOURS

Find the places where the curve is parallel to the y axis (undefined)
x^2+xy+y^2=7

Answer 1

@aum

Answer 2

take derivative
isolate y'
solve for denominator of derivative . That is where the curve // y axis

Answer 3

Ok, I have the derivative

Answer 4

But I don't know what to do with it

Answer 5

give me

Answer 6

Its -(2x+y)/(2y+x)

Answer 7

ok, let check
\((x^2+xy+y^2)'=7'\\
2x+y+xy'+2yy'=0\\2x +y+y'(x+2y)=0\)
\(y'=\dfrac{-x+2y}{2x+y}\)
that y' is slope of the curve, and when the curve //y-axis, y' is undefined
y' undefined when denominator =0 that mean 2x -y=0 or y = 2x

Answer 8

I think that you simplified that incorrectly

Answer 9

http://www.slader.com/textbook/9780132014083-calculus-graphical-numerical-algebraic-3rd-edition/163/exercises/50b/

Answer 10

I dont understand what they did here

Answer 11

Can you post the original problem?
they do dx/dy, not dy/dx

Answer 12

x^2+xy+y^2=7

Answer 13

I do dy/dx and dx/dx too

Answer 14

oh, I got it
they let minus sign in numerator, so that they have y = -2x
now replace y = -2x into the original one
\(x^2 +x(-2x)+4x^2=7\)
so that \(3x^2=7\\x = \pm\sqrt{7/3}\)
replace back to get y = \(\pm 2\sqrt{7/3}\)

Answer 15

Ok. What did they do after they got the derivative?

Answer 16

Going back a little bit. I want to work from there

Answer 17

after getting the derivative, let the denominator =0, solve for either x or y.

Answer 18

So they set x+2y equal to 0?

Answer 19

yes

Answer 20

Ok. One sec

Answer 21

I got y=-2x

Answer 22

Now what?

Answer 23

replace it into original problem, x^2+2xy +y^2 =7 to find x

Answer 24

Why?

Answer 25

because at that point (x), the curve //y-axis

Answer 26

Ok, I got 7

Answer 27

ok, let say
at y = -2x, y' is undefined.
y' is undefined --> curve // y-axis
at the curve, where are the point whose y= -2x? just replace to solve

Answer 28

Oh ok

Answer 29

how to get 7?

Answer 30

I didn't get 7, my bad

Answer 31

I got +-SQRT7/3

Answer 32

yes, that is x, right?
now plug back y = -2x to get y

Answer 33

Ok

Answer 34

Oh, great!! Thank you very very much!!!

Answer 35

hihihi:) glad to see you get it