The given curves are y = 3x2 and y = 2x3 + 1
dy/dx = 6x and dy/dx = 6x2
Since the given curves have common tangent, so their slopes are same.
Thus, 6x = 6x2.
⇒ x = 0 and 1.
when x = 0, y = 0 and when x = 1, y = 3.
So, the points are (0, 0) and (1, 3).
Hence, the equations of the common tangents are
y = 0 and y – 1 = 6(x – 1) = 6x – 6
⇒ y = 0 and y = 6x – 5.
