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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) 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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