AP Calculus ABmediummcq1 pt

For f(x)=x4f(x)=x^4, which statement about x=0x=0 is true?

A.ff has a point of inflection at x=0x=0 because f(0)=0f''(0)=0.
B.ff is concave down at x=0x=0 because f(0)=0f''(0)=0.
C.f(0)=0f''(0)=0, but ff has no point of inflection at x=0x=0 because ff'' does not change sign.
D.ff has a local maximum at x=0x=0.

Explanation

Core Concept

f(x)=12x2f''(x)=12x^2 is zero at x=0x=0 but positive on both sides, so the concavity never changes. A point of inflection requires a sign change of ff''.

Correct Answer

Cf(0)=0f''(0)=0, but ff has no point of inflection at x=0x=0 because ff'' does not change sign.

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