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  • Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 22

Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 22

Answers (1)

Answer:

f(x) is an increasing on the interval [4, 6].

Given:

f(x)=x^{2}-6x+3

To prove:

We have to prove that f(x) is an increasing on the interval [4, 6].

Hint:

A function f(x) is said to be increasing on [a, b] if f’(x) > 0.

Solution:

Given

f(x)=x^{2}-6x+3

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}\left(x^{2}-6 x+38\right) \\ &\Rightarrow f^{\prime}(x)=2 x-6 \\ &\Rightarrow f^{\prime}(x)=2(x-3) \\ \end{aligned}

\begin{aligned} &\text { Again, } x \in[4,6] \\ &\Rightarrow 4 \leq x \leq 6 \\ &\Rightarrow 1 \leq x-3 \leq 3 \\ &\Rightarrow(x-3)>0 \\ &\Rightarrow 2(x-3)>0 \\ &\Rightarrow f^{\prime}(x)>0 \end{aligned}

Thus f(x) is an increasing function x \in [4, 6]

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Gurleen Kaur

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