SOLUTION: For the curve given by 4x^2+y^2=48+2xy, show that there is a point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal.

Question 1107273: For the curve given by 4x^2+y^2=48+2xy, show that there is a point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal.
Found 2 solutions by Fombitz, greenestamps:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Differentiate implicitly to find the derivative,

Set the derivative equal to zero,

So when ,

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(2,8)
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So the tangent line is .
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Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Use implicit differentiation to find an expression for dy/dx and show that there is a value of y for which the derivative is zero when x is 2.

When x=2, the derivative is ; it is zero when y is 8.

The tangent to the graph at P(2,8) is horizontal.
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