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Explain solution rd sharma class 12 chapter 16 Increasing and decreasing function exercise multiple choice question, question 30

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Correct option (a)

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

Given:f(x)=x^{9}+3 x^{7}+64

Explanation:It is given that

f(x)=x^{9}+3 x^{7}+64     …..(i)

Differentiate (i) w.r.t  x

\begin{aligned} &f^{\prime}(x)=9 x^{8}+21 x^{6} \\ &f^{\prime}(x)=3 x^{6}\left(3 x^{2}+7\right) \end{aligned} 

\because f(x) is increasing

\Rightarrow 3 x^{6}\left(3 x^{2}+7\right)>0 

Thus, the given function is increasing on R


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