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  • Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 29 maths textbook solution

Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 29 maths textbook solution

Answers (1)

Answer:

f(x)=x-[x] is increasing in (0,1).

Given:

f(x)=x-[x]

To find:

We have to prove that f(x)=x-[x] is increasing in (0,1).

Hint:

For increasing function f ‘(x) > 0

Solution:

We have,

f(x)=x-[x]

We know that

\begin{aligned} &\text { For } x \in(0,1) \\ &\Rightarrow[x]=0 \\ &\therefore f(x)=x \end{aligned}

On differentiating both sides w.r.t. x we get,

\begin{aligned} &f^{\prime}(x)=1>0 \\ &\Rightarrow f^{\prime}(x)>0 \end{aligned}

Hence,f(x) is an increasing function for all x \in (0,1).

Posted by

Gurleen Kaur

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