GIVEN \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\] On differentiating w.r.t.x, we get \[f'(x)=3k{{x}^{2}}-18x+9\] For a function to be monotonically increasing. \[{{b}^{2}}-4ac<0\] Here, \[a=3k,b=-18,c=9\] \[\therefore {{b}^{2}}-4ac={{(-18)}^{2}}-4(3k)(9)\] \[=(-18)(-18)-(3k)18\times 2\] \[\Rightarrow 36-12k<0\Rightarrow k>3\]

"> GIVEN \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\] On differentiating w.r.t.x, we get \[f'(x)=3k{{x}^{2}}-18x+9\] For a function to be monotonically increasing. \[{{b}^{2}}-4ac<0\] Here, \[a=3k,b=-18,c=9\] \[\therefore {{b}^{2}}-4ac={{(-18)}^{2}}-4(3k)(9)\] \[=(-18)(-18)-(3k)18\times 2\] \[\Rightarrow 36-12k<0\Rightarrow k>3\]

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If \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\] is monotonically increasing in every interval, then which one of the following is correct?

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) . 10 months ago

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[c] GIVEN \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\] On differentiating w.r.t.x, we get \[f'(x)=3k{{x}^{2}}-18x+9\] For a function to be monotonically increasing. \[{{b}^{2}}-4ac<0\] Here, \[a=3k,b=-18,c=9\] \[\therefore {{b}^{2}}-4ac={{(-18)}^{2}}-4(3k)(9)\] \[=(-18)(-18)-(3k)18\times 2\] \[\Rightarrow 36-12k<0\Rightarrow k>3\]

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Posted on 17 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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