Question

consider the curve y^2 = 2 + (xy)

find all points on the curve where the line tangent to the curve has a slope of 1/2

Answer 1

\[y ^{2} = 2 + (xy)\]

Answer 2

I'll try to get the solution to this for you.

Answer 3

Actually, mimi should know. Help him mimi

Answer 4

hm, i don't know sorry. i thought i knew :/

Answer 5

So mimi, you don't know basic math or calculus

Answer 6

:o this one has my entire class stumped and the teacher wont give us the answer

Answer 7

this looks like implicit differentiation.
I know calculus but not this.

Answer 8

yeah you have to implicitly differentiate the equation then set it equal to .5 i think but not sure where to go after that

Answer 9

If you know how to get to that point, then do it. Maybe we can help you from there.

Answer 10

\[dy/dx = y /(2y-x)\] thing is they dont give you anything to find a point on the graph so im thinking if you solve the original for x and substitute it might work

Answer 11

That sounds like a good idea

Answer 12

\[1/2 = y /(2y - (y ^{2} -2 /y))\]

Answer 13

i get stuck about here because I cant algebra and / or you cant do that XD

Answer 14

I see, well, hopefully, what you've done is correct so far.

Answer 15

After doing the math I get

\[y = \sqrt[3]{2}\]

I can show you what I did

Answer 16

ok

Answer 17

I will post a vyew. You're going to laugh when you see how easy it is

Answer 18

http://vyew.com/room#/418625/Open_Study

Answer 19

haha it probably is pretty easy i just get hung up on basic math like when you have like x + 3/x^2

Answer 20

You did a good job too. Couldn't have done it without you :P

Answer 21

The coordinates of the solution points are:\[\left(0,\sqrt{2}\right),\left(0,-\sqrt{2}\right) \]Refer to the Mathematica attachment.