anonymous
  • anonymous
Show that the curve defined implicitly by the equation xy^3 + x^3y=4 has no horizontal tangent
Mathematics
jamiebookeater
  • jamiebookeater
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asnaseer
  • asnaseer
you can rewrite your equation as:\[xy(y^2+x^2)=4\]from this we can observe that x or y cannot be zero - agreed?
asnaseer
  • asnaseer
when and if you come back to this question and if you agree with the statement above, then you should use implicit differentiation to calculate the derivative of the function given to you. you will find that the derivative can never be equal to zero which would imply that the given curve has no horizontal tangents.
anonymous
  • anonymous
OK so I found the derivative

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anonymous
  • anonymous
Do I set it equal to zero ?
asnaseer
  • asnaseer
yes, tangents are found by setting the derivative to zero and then finding what values satisfy that equation.

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