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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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