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If \( m \) is the minimum value of \( k \) for which the function \( f(x)=x \sqrt{k x-x^{2}} \) is increasing in the interval \( [0,3] \) and \( \mathrm{M} \) is the maximum value of \( f \) in \( [0,3] \) when \( k=m \), then the ordered pair ( \( \mathrm{m}, \mathrm{M} \) ) is equal to :
|JEE Main - 2019(April)|
(1) \( (4,3 \sqrt{2}) \)
(2) \( (4,3 \sqrt{3}) \)
\( (3)(3,3 \sqrt{3}) \)
\( (4)(5,3 \sqrt{6}) \)
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