Show that the tangents to the curve `y=7x^3+11` at the points where `x = 2` and `x = -2` are parallel.

Explanation

The equation of the given curve is `y=7x^3+11`

`implies dy/dx=21x^2`

Thus the slope of the tangent to a curve at x=2 is `(dy/dx)_(x=2)=(21x^2)_(x=2)=84`

and slope of the tangent to a curve at x=−2 is `(dy/dx)_(x=-2)=(21x^2)_(x=-2)=84`

It is observed that the slopes of the tangents at both the are equal.
Hence, the two tangents are parallel.