Determining Concavity

AP Calculus AB· difficulty 2/5

For f(x)=x36x2+9xf(x) = x^3 - 6x^2 + 9x, on what interval is ff concave up?

  • A

    (,1)(-\infty, 1)

  • B

    (1,3)(1, 3)

  • C

    (,2)(-\infty, 2)

  • D

    (2,)(2, \infty)

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Explanation

f(x)=6x12>0x>2f''(x) = 6x - 12 > 0 \Leftrightarrow x > 2.

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