hey try this...
The only possible inflexion points will happen where
(d2y)/( dx2) = 0
From specified function as:
(dy)/(dx) = 3x2 and (d2y)/( dx2) = 6x
Equating the second derivative to zero, we include
6x = 0 or x = 0
We test whether the point at that x = 0 is an inflexion point as follows
While x is slightly less than 0, ((d2y)/(dx2)) < 0; it means a downward concavity
While x is slightly larger than 0, ((d2y)/(dx2)) > 0; it means an upward concavity
Hence we have a point of inflexion at point x = 0 since the concavity of the curve changes as we pass from the left to the right of x = 0