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  • Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 26

Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 26

Answers (1)

Correct option (b)

Hint: First differentiate Q(x) w.r.to then using the relation between {f}'{x} & f(2a-x)identify type of Q(x)

Given:Q(x)=f(x)+f(2 a-x)

Explanation:It is given that

Q(x)=f(x)+f(2 a-x)                                                                                                  …..(i)

Differentiate (i) w.r.t  x

Q^{\prime}(x)=f^{\prime}(x)-f^{\prime}(2 a-x) 

Since f^{\prime}(x)>0 \Rightarrow f^{\prime \prime}(x)>0

Here x\epsilon \left [ 0,a \right ]

\begin{aligned} &x \leq 2 a-x \\ &f^{\prime}(x) \leq f^{\prime}(2 a-x) \end{aligned} 

Also, Q^{\prime}(x)=f^{\prime}(x)-f^{\prime}(2 a-x)

Q(x) is decreasing on [0,a]

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