anonymous
  • anonymous
Show that the curve defined implicitly by the equation xy^3 + x^3y=4 has no horizontal tangent
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.