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abraham95x
 3 years ago
Show that the curve defined implicitly by the equation xy^3 + x^3y=4 has no horizontal tangent
abraham95x
 3 years ago
Show that the curve defined implicitly by the equation xy^3 + x^3y=4 has no horizontal tangent

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asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3you 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
 3 years ago
Best ResponseYou've already chosen the best response.3when 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.

abraham95x
 3 years ago
Best ResponseYou've already chosen the best response.0OK so I found the derivative

abraham95x
 3 years ago
Best ResponseYou've already chosen the best response.0Do I set it equal to zero ?

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3yes, tangents are found by setting the derivative to zero and then finding what values satisfy that equation.
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