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  • Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 20 maths

Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 20 maths

Answers (1)

Answer:

f(x) \text { is an increasing function for all }x \: \in \: R

Given:

f(x)= x^{9}-4x^{7}+11

To prove:

\text { We have to show that }f(x) \text { is an increasing function for all }x \: \in \: R

Hint:

f’(x) > 0 is condition for increasing function of f(x).

Solution:

Given

f(x) x^{9}-4x^{7}+11

On differentiating both sides w.r.t x we get

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}\left(x^{9}-4 x^{7}+11\right) \\ &\Rightarrow f^{\prime}(x)=9 x^{8}-28 x^{6} \\ &\Rightarrow f^{\prime}(x)=x^{6}\left(9 x^{2}+28\right) \\ &\text { As given, } x \in R \\ &\Rightarrow x^{6}>0 \text { and } 9 x^{2}+28>0 \\ &\Rightarrow x^{6}\left(9 x^{2}+28\right)>0 \\ &\Rightarrow f^{\prime}(x)>0 \end{aligned}

Hence, condition for fx to be increasing

\text { Thus }f(x) \text { is an increasing on interval }x \: \in \: R

Posted by

Gurleen Kaur

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