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An inflection point is where the concavity changes, which requires the second derivative to change sign. A zero second derivative alone is not enough; the sign must actually flip.
Inflection point
f''(x) = 0 with a sign change in f'' on either side
f'' = 6x − 12, so the inflection point is at x = 2 where f = 3.
For x⁴ the second derivative vanishes at 0 but does not change sign, so the curve stays concave up throughout.