For f(x)=x4−4x3f(x) = x^4 - 4x^3f(x)=x4−4x3, find the inflection points and intervals of concavity.
Inflection at x=0x=0x=0 and x=2x=2x=2; concave up on (−∞,0)∪(2,∞)(-\infty,0)\cup(2,\infty)(−∞,0)∪(2,∞), concave down on (0,2)(0,2)(0,2)
Inflection at x=2x=2x=2 only; concave up everywhere else
Inflection at x=3x=3x=3; concave up for x>3x>3x>3
No inflection points