At what point on the curve y = x^3 - 3x^2 + 2 does the inflection point occur?
Answer and explanation
Correct answer: C. (1, 0)
- Step 1: First derivative: dy/dx = 3x^2 - 6x. Second derivative: d^2y/dx^2 = 6x - 6. Step 2. Set d^2y/dx^2 = 0 => 6x = 6 => x = 1. Find y: y = 1^3 - 3(1)^2 + 2 = 1 - 3 + 2 = 0. Point is (1, 0). Answer: (1, 0). Why not the others: At x = 2, dy/dx = 0, which is a local minimum, not the inflection point.
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