Consider y = 2x3 – 4 as the equation of curve
By differentiating both sides w.r.t. x
dy/dx = 6x2
We get
(dy/dx)x=2 = 6(2)2 = 24
When m1 = 24
dy/dx = 6x2
(dy/dx)x=2 = 6(2)2 = 24
Similarly when m2 = 24
dy/dx = 6x2
(dy/dx)x=-2 = 6(-2)2 = 24
Hence the tangents to the curve at the points x = 2 and x = -2 are parallel i.e. m1 = m2.