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Implicit Differentiation Tangent lines

  • Thread starter htoor9
  • Start date
  • #1
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Homework Statement



Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line.

Homework Equations



dy/dx dx/dy or something not sure.

The Attempt at a Solution



Well I know that a horizontal tangent line would mean the slope is zero...but what exactly do I do?
 

Answers and Replies

  • #2
33,646
5,313

Homework Statement



Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line.

Homework Equations



dy/dx dx/dy or something not sure.

The Attempt at a Solution



Well I know that a horizontal tangent line would mean the slope is zero...but what exactly do I do?
The easiest thing to do is to use implicit differentiation to get dy/dx, then set it to zero. Since the graph is an ellipse, there should be two points where dy/dx = 0.
 

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