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  • Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 32 maths textbook solution

Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 32 maths textbook solution

Answers (1)

Answer:

f(x) is strictly increasing on R.

Given:

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

To prove:

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

Hint:

For f(x) to be increasing we must have f’(x) > 0.

Solution:

Here we have

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

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}\left(x^{3}-3 x^{2}+4 x\right) \\ &\Rightarrow f^{\prime}(x)=3 x^{2}-6 x+4 \\ &\Rightarrow f^{\prime}(x)=3\left(x^{2}-2 x+1\right)+1 \\ &f^{\prime}(x)=3(x-1)^{2}+1 \\ &\text { Here } 3(x-1)^{2}+1>0 \text { for all } x \in R \end{aligned}

Hence f(x) is strictly increasing function on R.

Posted by

Gurleen Kaur

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