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  • Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 23

Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 23

Answers (1)

Correct option (d)

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

Given: f(x)=\frac{\lambda \sin x+2 \cos x}{\sin x+\cos x}

 

Explanation:It is given that

f(x)=\frac{\lambda \sin x+2 \cos x}{\sin x+\cos x} …..(i)

Differentiate (i) w.r.t  x

\begin{aligned} &f^{\prime}(x)=(\lambda-2) \sin ^{2} x+(\lambda-2) \cos ^{2} x>0 \\ &f^{\prime}(x)=(\lambda-2)\left(\sin ^{2} x+\cos ^{2} x\right) \\ &f^{\prime}(x)=(\lambda-2)>0 \\ &\therefore \lambda>2 \end{aligned} 

So, the function is increasing if\begin{aligned} & \lambda>2 \end{aligned}

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