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

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asnaseerBest ResponseYou've already chosen the best response.3
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?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.3
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.
 one year ago

abraham95xBest ResponseYou've already chosen the best response.0
OK so I found the derivative
 one year ago

abraham95xBest ResponseYou've already chosen the best response.0
Do I set it equal to zero ?
 one year ago

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