Find the inflection point of the cubic curve y = x^3 - 6x^2 + 9x + 2.
Answer and explanation
Correct answer: A. (2, 4)
- Step 1: Find the second derivative: y' = 3x^2 - 12x + 9, and y'' = 6x - 12.
- Step 2: Set y'' = 0: 6x = 12 implies x = 2. Substitute into y: y(2) = 2^3 - 6(2^2) + 9(2) + 2 = 8 - 24 + 18 + 2 = 4.
Answer
(2, 4).
Why not the others: '(2, 0)' computes an incorrect y-coordinate; '(1, 6)' is a local maximum; '(3, 2)' is a local minimum.
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