A) \[(4,3\sqrt{2})\]
B) \[(4,3\sqrt{3})\]
C) \[(3,3\sqrt{3})\]
D) \[(5,3\sqrt{6})\]
Correct Answer: B
Solution :
\[f(x)=x\sqrt{kx-{{x}^{2}}}\] \[f'(x)=\frac{3kx-4{{x}^{2}}}{2\sqrt{kx-{{x}^{2}}}}\]For\[\uparrow f'(x)\ge 0\] \[kx-{{x}^{2}}\ge 0\] | \[3kx-4{{x}^{2}}\ge 0\] \[4{{x}^{2}}-3kx\le 0\] |
\[{{x}^{2}}-kx\le 0\] | \[4x(x-\frac{3k}{4})\le 0\] |
\[x(x-k)\le 0\]so\[x\in [0,3]\] | \[3-\frac{3k}{4}\le 0\] |
\[+\text{v}e\] | \[\] |
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