Curve Sketching

AP Calculus AB· difficulty 2/5

For f(x)=x3f(x) = x^3, the function is

  • A

    Always increasing, with inflection at x=0x = 0

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  • B

    Concave up for x<0x < 0, concave down for x>0x > 0

  • C

    Always decreasing

  • D

    Both A and not C

Explanation

f(x)=3x20f'(x) = 3x^2 \ge 0 — increasing (strictly except at x=0x = 0). f(x)=6xf''(x) = 6x changes sign at 00 — inflection.

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