Find the points on the curve y = x - 12x + 6 where the tangent line is horizontal. y Solution Horizontal tangents occur where the derivative is zero. We have dy a ( x 2 ) + 0 ( 6 ) dx dx dx dx 4x Thus = 0 if x = 0 or = 0, that is, x = + So the given curve has horizontal tangents when x = enter your dx answers as a comma-separated list). The corresponding points are then the following. smallest x-value (x, y) = ( x, y ) = largest x-value ( x , y ) =