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  • Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 13

Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 13

Answers (1)

Correct option (b)

Hint: Use the condition for f(x),

{f}'(x)>0 , f(x) is increasing

{f}'(x)<0 ,f(x)  is decreasing

Given:f(x)=2|x-1|+3|x-2|

Explanation: We need to checkf(x)  in interval (1,2)

Here, f(x)=2|x-1|+3|x-2|

\because x\epsilon (1,2)  So, x>1  & x<2

\begin{aligned} &\Rightarrow x-1>0 \& x-2<0 \\ &f(x)=2|x-1|+3|x-2| \\ &f(x)=2(x-1)+3(x-2) \\ &f(x)=2 x-2-3 x+6 \\ &f(x)=-x+4 \\ &f^{\prime}(x)=-1<0 \end{aligned}

Thus, f(x) is monotonically decreasing in the interval (1,2)

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