Question

Show that the tangents to the curve y = 7x³ + 11 at the points where x = 2 and x = −2 are parallel.

Answer 1

The equation of the given curve is y = 7x³ + 11.

The slope of the tangent to a curve at (x₀, y₀) is  

Therefore, the slope of the tangent at the point where x = 2 is given by,

It is observed that the slopes of the tangents at the points where x = 2 and x = −2 are equal.

Hence, the two tangents are parallel.