If 3x^2-2y^2=4xy + 20, find the point(s) at which the graph from Problem 28 has vertical tangents. I found that dy/dx= (3x-2y)/(2x+2y), but now I don't know what to do. Do I set dy/dx to 0?

Answer 1

For a vertical line, the slope would be undefined, that is,
(3x-2y)/(2x+2y) has to be undefined.
When does that happen?
When the denominator is zero, so
2x + 2y = 0
y = -x

sub into the origianal
3x^2 - 2(-x)^2 = 4x(-x) + 20
5x^2 = 20
x^2=4
x = ±2

if x=2, y = -2,
if x = -2, y = 2

points where tangent is vertical are (2,-2) and (-2,2)

Answer 2

thanks! that was really helpful ;)