baldymcgee6
  • baldymcgee6
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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myininaya
  • myininaya
Do you know how to find the derivative?
baldymcgee6
  • baldymcgee6
Yeah, do we just find the derivative and plug in the points?
myininaya
  • myininaya
Yes find the derivative of both sides with respect to x And then replace x with 2 and y with 1

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baldymcgee6
  • baldymcgee6
What does this part of the question mean? y=f(x), near x=2, y =1.
anonymous
  • anonymous
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
  • anonymous
in practical value, you can ignore that statement and proceed as myininaya said
baldymcgee6
  • baldymcgee6
Ahh, thank you satellite, makes more sense now.
myininaya
  • myininaya
But this point isn't even on the curve.....
baldymcgee6
  • baldymcgee6
@myininaya \[2xy+x^2y'+2y^3+2x3y^2y' = 0\] I got this when I differentiated both sides, but how do I get y'?
baldymcgee6
  • baldymcgee6
@satellite73 ?
baldymcgee6
  • baldymcgee6
Nevermind, got it! Thanks guys

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