Consider
f(x)=x4−4x3+6x2+5f(x) = x^4 - 4x^3 + 6x^2 + 5f(x)=x4−4x3+6x2+5
An inflection point is an input where the concavity of fff actually changes — cup turning into cap, or cap turning into cup.
Which statement about the inflection points of fff is correct?
Select all that apply.
x=1x = 1x=1 is the only inflection point, because f′′(1)=0f''(1) = 0f′′(1)=0.
x=0x = 0x=0 and x=2x = 2x=2 are both inflection points.
x=0x = 0x=0 is an inflection point, because the curve flattens there (f′(0)=0f'(0) = 0f′(0)=0).
fff has no inflection point at all: f′′(x)=12(x−1)2≥0f''(x) = 12(x-1)^2 \ge 0f′′(x)=12(x−1)2≥0 everywhere, so the concavity never changes.