EXAMPLE 6 Find the points on the curve y = x4 - 8x2 + 4 where the tangent line is horizontal. SOLUTION Horizontal tangents occur where the derivative is zero. We have dy dx dx 8- 2 ( 4 ) 4x X X Thus dy/dx = 0 if x = 0 or = 0, that is, x = .So the given curve has horizontal tangents when x = (enter Video Example () your answers as a comma-separated list). The corresponding points are then the following. ( x, y ) = (smallest x-value) ( x , V ) = ( x, y ) = (largest x-value)