Consider the function $f(x)=6x^3-x^4.$ Which of the following is NOT true?

$f$ has local extrema at $x=0$ and $x=\frac{9}{2}$

$f$ is increasing on the interval $(0,\frac{9}{2})$

$f$ has inflection points at $x=0$ and $x=3$

The sign of $f$ changes from positive to negative at $x=6$

$f$ is increasing on the interval $(-,0)$

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