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  • Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 16

Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 16

Answers (1)

Correct option (c)

Hint: If f(x)  is increasing function {f}'(x)>0

Given: f(x)=k x^{3}-9 x^{2}+9 x+3

Explanation:It is given that

f(x)=k x^{3}-9 x^{2}+9 x+3 …..(i)

Differentiate (i) w.r.t  x

{f}'(x)=3 k x^{2}-18 x+9

\because f(x) is increasing {f}'(x)>0

\begin{aligned} &3 k x^{2}-18 x+9>0 \\ &k x^{2}-6 x+3>0 \end{aligned}

If a>0\Rightarrow b^{2}-4ac<0

So, (-6)^{2}-4.k.3<0

\begin{aligned} &36-12 k<0 \\ &3-k<0 \\ &k>3 \end{aligned} 

Thus, the function is monotonic increasing if k>3

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