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Provide solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Very short answer type question  6

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Answer: Does not exist

Hint: if f(x) is differentiable at x=2 then \lim _{x \rightarrow c} \frac{f(x)-f(2)}{x-2}=f^{\prime}(2)


Explanation:f(x)=\left(\begin{array}{ll} x-2 & x \geq 2 \\ -(x-2) & x<2 \end{array}\right)

Now, LHD at x=2

        \lim _{x \rightarrow 2^{-}} \frac{f(x)-f(2)}{x-2}=\lim _{h \rightarrow 0} \frac{-(2-h-2)-0}{-h}

\begin{aligned} &=-1 \\\\ &\text { RHD at\; x }=2 \\\\ &\lim _{x \rightarrow 2^{+}} \frac{f(x)-f(2)}{x-2}=\lim _{x \rightarrow 2} \frac{(2+h-2)-0}{h} \\\\ &\text { As } L H D \neq R H D \end{aligned}

f(x) is not differentiable so f^{'}(2) does not exist.

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