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Home / So \( x = 1 \) and \( x = 3 \) are critical points.

So \( x = 1 \) and \( x = 3 \) are critical points.

February 22, 2026

$So \( x = 1 \) and \( x = 3 \) are critical points.$

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\( f'(x) = 3x^2 - 12x + 9 \).
Setting \( f'(x) = 0 \) for critical points:
3x^2 - 12x + 9 = 0 \Rightarrow x^2 - 4x + 3 = 0 \Rightarrow (x-3)(x-1) = 0
Check \( f(1) = 2 \):
f(1) = 1^3 - 6(1)^2 + 9(1) + c = 1 - 6 + 9 + c = 4 + c
+ c = 2 \Rightarrow c = -2

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