Get Answers to all your Questions

header-bg qa

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

Posted by

Info Expert 29

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support