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

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

Answers (1)

Answer:

f(x) is an increasing on R.

Given:

f(x)=4x^{3}-18x^{2}+27x-27

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:

Here we have

f(x)=4x^{3}-18x^{2}+27x-27

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}\left(4 x^{3}-18 x^{2}+27 x-27\right) \\ &\Rightarrow f^{\prime}(x)=12 x^{2}-36 x+27 \\ &\Rightarrow f^{\prime}(x)=3\left(4 x^{2}-12 x+9\right) \\ &\Rightarrow f^{\prime}(x)=3(2 x-3)^{2} \end{aligned}

\begin{aligned} &\text { Now, } x \in R \\ &\Rightarrow(2 x-3)^{2}>0 \\ &\Rightarrow 3(2 x-3)^{2}>0 \\ &\Rightarrow f^{\prime}(x)>0 \end{aligned}

Thus f(x) is increasing function on R.

Posted by

Gurleen Kaur

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