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If $f(x)=k x^3-9 x^2+9 x+3$ is monotonically increasing in each interval, then
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Verified Answer
The correct answer is:
$k\gt3$
$f^{\prime}(x)=3 k x^2-18 x+9=3\left[k x^2-6 x+3\right]\gt0, \forall x \in R$
$\therefore \Delta=b^2-4 a c \lt 0, k\gt0$ i.e., $36-12 k \lt 0$ or $k\gt3$
$\therefore \Delta=b^2-4 a c \lt 0, k\gt0$ i.e., $36-12 k \lt 0$ or $k\gt3$
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