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Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 20

Answers (1)

Correct option (b)

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

And decreasing if {f}'(x)>0

Given: f(x)=2|x-1|+3|x-2| in the interval (1,2)

Explanation:It is given that


In the interval (1,2) , we can write

|x-1|=x-1 \&|x-2|=-(x-2)

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

 So, the given function is decreasing.

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