# Math Help - implicit differentiation (horizontal tangent line)

1. ## implicit differentiation (horizontal tangent line)

Given the curve $x^2+xy+y^2=9$

a) Find $y'$

$x^2+xy+y^2=9$

Taking the derivative of the above equation and using product rule for xy, i get,
$2x+(y+xyy')+2yy' = 0$
$xy'+2yy' = -2x-y$
$y'(x-2y)=-2x-y$

$y' = (-2x-y)/(x+2y)$

b) Find all points on the curve at which the tangent line is horizontal

Is a) correct? and also how do i do letter b)? i have no clue what to do. thanks!

2. To find the points that are horizontally tangent find y' of 0.

0=(-2x-y)/(x+2y)

Because the slope will be zero when it is horizontally tangent.

Hope it helps.

3. oh okay, but im still totally lost, what do i do after that?

4. Solve you x and y and plug them into point slope form.