## baldymcgee6 2 years ago The equation x^2y+2xy^3=8 defines y as a function of x, y=f(x), near x=2, y =1. Find the slope of the curve x^2y+2xy^3=8 when x=2, y=1

1. myininaya

Do you know how to find the derivative?

2. baldymcgee6

Yeah, do we just find the derivative and plug in the points?

3. myininaya

Yes find the derivative of both sides with respect to x And then replace x with 2 and y with 1

4. baldymcgee6

What does this part of the question mean? y=f(x), near x=2, y =1.

5. satellite73

it means that the curve itself might not represent a function, because it does not pass the "vertical line test" but "locally" it is a function, that is, near the point it does represent a function hello @myininaya!

6. satellite73

in practical value, you can ignore that statement and proceed as myininaya said

7. baldymcgee6

Ahh, thank you satellite, makes more sense now.

8. myininaya

But this point isn't even on the curve.....

9. baldymcgee6

@myininaya \[2xy+x^2y'+2y^3+2x3y^2y' = 0\] I got this when I differentiated both sides, but how do I get y'?

10. baldymcgee6

@satellite73 ?

11. baldymcgee6

Nevermind, got it! Thanks guys