Implicit Derivative Question: Finding points on curve

[grapz]

Given the curve x^2 + xy + y^2 = 7

Find points on the curve where the tangents are parallel to the x-axis.


Basically from my understanding i have to find points where the slope is 0.

i found the derivative which is - (2x + y)/ x +2y

i do not no how to solve for x and y. thx

 

[stapel]

Hint: A fraction is zero when its numerator is zero.

Eliz.

 

[grapz]

how can the numerator be zero?

i am not sure, because it says the tangent is parelle so its slope is same, but it doesnt' give you any points so i'm not sure what to do

 

[stapel]

how can the numerator be zero?

I'm sorry, but I'm not sure what you mean by this...?

For the tangent to be horizontal, the tangent line must have a slope of zero, which means dy/dx must be zero (at that point), which means the numerator of the rational expression for dy/dx must be zero. So set it equal to zero and solve.

Eliz.

 

[skeeter]

Given the curve x^2 + xy + y^2 = 7

Find points on the curve where the tangents are parallel to the x-axis.


Basically from my understanding i have to find points where the slope is 0.

i found the derivative which is - (2x + y)/ x +2y

i do not no how to solve for x and y. thx

slope = dy/dx = 0

if -(2x+y)/(x+2y) = 0, then y = -2x

substitute -2x for y in the original equation of the curve ...

x^2 + x(-2x) + (-2x)^2 = 7

now, solve for x ... then find the points (x,y) on the curve where dy/dx = 0.