math
posted by alison on .
question: find the points at which the graph of x^2 4x + y62 6y =12 has a vertical or horizontal tangent line.
I found the deriviative to be (x2)/(3y)
Then, the x value for a horizontal would be x=2 and the y value for a vertical would be y=3.
But how do i find the exact points. My teacher gave me these answers
Horizontal tangent at (2,8) and (2,2)
Vertical tangent at (7,3) and (3,3)
But i don't understand how she got those points. can someone show me?
Thanks

You've done the hard part, so you're probably just overthinking it! :)
When x=2, plug 2 into that equation of the circle, and what do you get?
x^2 4x + y^2 6y =12
4  8 + y^2 6y = 12
y^2 6y 16 = 0
and solve for y.
Same method works for getting the points where y=3.