AP Calculus ABeasymcq1 pt

Which statement correctly describes the graph of f(x)=x3f(x)=x^3?

A.ff is increasing for all xx and has a point of inflection at (0,0)(0,0).
B.ff is decreasing for all xx.
C.ff has a local maximum at (0,0)(0,0).
D.ff is concave up for all xx.

Explanation

Core Concept

f(x)=3x20f'(x)=3x^2\ge 0, so ff is increasing everywhere, and f(x)=6xf''(x)=6x changes sign at x=0x=0. So the graph has a point of inflection at (0,0)(0,0).

Correct Answer

Aff is increasing for all xx and has a point of inflection at (0,0)(0,0).

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