Find the coordinates of the inflection point for the function f(x) = x^3 - 6x^2 + 9x + 2.
Answer and explanation
Correct answer: A. (2, 4)
- Step 1: f'(x) = 3x^2 - 12x + 9; f''(x) = 6x - 12. Step 2. Set f''(x) = 0 => 6x = 12 => x = 2. Since f''(x) changes sign at x = 2, it is an inflection point. f(2) = 8 - 24 + 18 + 2 = 4. Answer: (2, 4). Why not the others: An inflection point occurs where the second derivative changes sign.
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