Find all the points on the leminiscate where the tangent line is horizontal.
Working with the LaTex as image files is proving a little limiting, so hopefully I have the most salient steps included.
Ok, so the derivative of the equation is:
And since I want the horizontals, I want the values (dy/dx)=0. I figured that since 0/anything = 0, I just need the values of x and y that make the numerator 0.
So I set the numerator of the derivative equal to zero and solved for y:
But when I plug that into the original equation, it doesn't work -- I get 4 = 8. Also, just looking at the equations, it seems like (±1,±1) should work, but it makes the orignial eqation untrue as well. Any help is greatly appreciated!