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

Question

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

myininaya · Answer

Do you know how to find the derivative?

baldymcgee6 · Answer

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

myininaya · Answer

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

baldymcgee6 · Answer

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

anonymous · Answer

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!

anonymous · Answer

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

baldymcgee6 · Answer

Ahh, thank you satellite, makes more sense now.

myininaya · Answer

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

baldymcgee6 · Answer

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

baldymcgee6 · Answer

@satellite73 ?

baldymcgee6 · Answer

Nevermind, got it! Thanks guys