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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)>0f(x) is increasing

{f}'(x)<0 ,f(x)  is decreasing


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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