So the intervals are (-∞, -2), (-2, 1)(1, ∞)
When x ∈ (-∞, -2) say x = -3
d2y/dx2 = 12(2 + 3 - 9) = 12(-4) > 0
The curve is concave upward.
When x ∈ (-2, 1) say x = 0.
d2y/dx2 = 12(2 - 0 - 0) = 24 > 0
⇒ The curve is concave upward.
x = -2 is a point of inflection.
When x ∈ (1,∞) say x = 2
d2y/dx2 = 12(2 - 2 - 4) = 12(-4) < 0
⇒ The curve is convex upward. So, x = 1 is a point of inflection.
At x = – 2, y = 12(4) – 2(-8) – (16) = 48 + 16 – 16 = 48
At x = 1, y = 12(1) – 2(1) – 1 = 12 – 2 – 1 = 9
So, the points of inflection are (1, 9) and (-2, 48)