horizontal tangent lines pls help!

[aayushma34]

m4

www.desmos.com

can someone tell me how many horizontal tangent lines there are? Idk if it's one or three !!

 

[skeeter]

well, the orange line is not horizontal, yet the blue graph has how many local extrema?

 

[Dr.Peterson]

m4

www.desmos.com

can someone tell me how many horizontal tangent lines there are? Idk if it's one or three !!

Presumably you are asking for the number of points at which the tangent to [MATH]2x^{2}y-xy^{3}+3y=3[/MATH] is horizontal.

Do you have a reason to think it is only one? Please explain why you are asking.