Question

what are the points where a vertical and a horizontal tangenet line occur on the curve x+y^2-y=1. If none, explain. I used implicit differentiation to get 1/1-2y. where do i go from there?

Answer 1

a vertical line is defined when dx/dy = 0

a horizontal line is defined when dy/dx = 0

Answer 2

x+y^2-y=1

x' + 2yy' -y' = 0



dx/dy: x' + 2y -1 = 0

dy/dx: 1 + y'(2y-1) = 0

Answer 3

2y-1 = 0

and

1/(1-2y) = 0 this might not work out

Answer 4

hmm
x = 1+y -y^2

x' = 1 - 2y = 0 when y=1/2

pfft, we have a parabola on its side, no wonder theres no horizontal line