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  • Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 25

Need solution for rd sharma maths class 12 chapter 16 Increasing and Decreasing functions exercise Multiple choice question, question 25

Answers (1)

Correct option (b)

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

Given: f(x)=\log _{a} x

Explanation:It is given that

f(x)=\log _{a} x 

\Rightarrow a^{f(x)}=x …..(i)

Differentiate (i) w.r.t  x

\begin{aligned} &\Rightarrow a^{f(x)} \cdot \log a \cdot f^{\prime}(x)=1 \\ &\Rightarrow f^{\prime}(x)=\frac{1}{a^{f(x)} \cdot \log a} \\ &\Rightarrow f^{\prime}(x)=\frac{1}{x \log a} \end{aligned}

 

Since the function is increasing on R

 

\begin{aligned} &\frac{1}{x \log a}>0 \\ &\Rightarrow a>1 \end{aligned} 

Thus the function is increasing if \begin{aligned} & a>1 \end{aligned}

 

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