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If $f (x) = {kx}^{3} - 9 x^{2} + 9 x + 3$ is monotonically increasing in R, then

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k<3

k≤3

k≥2

none of these

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detailed solution

Correct option is C

f′(x)=3kx2−18x+9=3kx2−6x+3≥0∀x∈R or D=b2−4ac≤0,k>0, i.e., 36−12k≤0 or k≥3

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If f(x)=kx3−9x2+9x+3is monotonically increasing in R, then

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If $f (x) = {kx}^{3} - 9 x^{2} + 9 x + 3$ is monotonically increasing in R, then