Show that the tangents to the curve y = 2x3 – 4 at the points x = 2

1.	Show that the tangents to the curve y = 2x3 – 4 at the points x = 2 and x = – 2 are parallel.
Answer» 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.

Show that the tangents to the curve y = 2x3 – 4 at the points x = 2 and x = – 2 are parallel.

Answer»

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.