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  • Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 30 subquestion (i)

Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 30 subquestion (i)

Answers (1)

Answer:

f(x) is an increasing on R

Given:

f(x)=3x^{5}+40x^{3}+240x

To prove:

We have to prove that f(x) is an increasing on R.

Hint:

If f’(x) > 0 then f(x) is increasing function.

Solution:

Given

f(x)=3x^{5}+40x^{3}+240x

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}\left(3 x^{5}+40 x^{3}+240 x\right) \\ &\Rightarrow f^{\prime}(x)=15 x^{4}+120 x^{2}+240 \\ &\Rightarrow f^{\prime}(x)=15\left(x^{4}+8 x^{2}+16\right) \\ &\Rightarrow f^{\prime}(x)=15\left(x^{2}+4\right)^{2} \end{aligned}

\begin{aligned} &\text { Now, } x \in R \\ &\Rightarrow\left(x^{2}+4\right)^{2}>0 \\ &\Rightarrow 15\left(x^{2}+4\right)^{2}>0 \\ &\Rightarrow f^{\prime}(x)>0 \end{aligned}

Thus f(x) is increasing function for all x \in R.

Posted by

Gurleen Kaur

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