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If the function $f (x) = K x^{3} - 9 x^{2} + 9 x + 3$ is monotonically increasing, then

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$K < 3$

$K \leq 2$

$K \geq 3$

$K \leq 1$

answer is C.

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Detailed Solution

$f^{1} (x) = 3 K x^{2} - 18 x + 9 f^{1} (x) \geq 0 \Rightarrow 3 K x^{2} - 18 x + 9 \geq 0 \Rightarrow K x^{2} - 6 x + 3 \geq 0 Δ \leq 0 \Rightarrow 36 - 12 k \leq 0 \Rightarrow 3 - K \leq 0 \Rightarrow K \geq 3$

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