alleryFor y = x³ - 6x² + 9x, find critical points (where y' = 0):
Ax = 1, 3 (where y' = 3x² - 12x + 9 = 0)
Bx = -1, -3
Cx = 6
Dx = 0 only
Answer & Solution
Correct answer: A. x = 1, 3 (where y' = 3x² - 12x + 9 = 0)
We have y' = 3x² - 12x + 9.
That is y' = 3(x² - 4x + 3).
So y' = 3(x - 1)(x - 3).
**Critical points:** x = 1, 3. Second derivative test: y'' = 6x - 12. At x = 1: y'' = -6 (max).
At x = 3: y'' = 6 (min).
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