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  • Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Multiple choice question 23

Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Multiple choice question 23

Answers (1)

Answer:

        None of these

Hint:

        In case of function of one variable it’s a function that doesn’t have finite derivation

Given:

        f(x)=\sqrt{x^{2}-10 x+25}, f^{\prime}(x)=

Solution:  

        f(x)=\sqrt{x^{2}-10 x+25}

                  \begin{aligned} &=\sqrt{(x-5)^{2}} \\\\ &=|x-5| \end{aligned}

f(x)=\left\{\begin{array}{cll} x-5 & \text { for } & x>5 \\\\ -(x-5) & \text { for } & x<5 \end{array}\right.

L H D=\lim _{x \rightarrow 5^{-}} \frac{f(x)-f(a)}{x-a}

            =\lim _{x \rightarrow 5^{-}} \frac{\sqrt{x^{2}-10 x+25}-\sqrt{5^{2}-10(5)+25}}{x-5}

            =\lim _{x \rightarrow 5^{-}} \frac{|x-5|}{(x-5)}=\lim _{x \rightarrow 5^{-}} \frac{-(x-5)}{x-5}=-1

R H D=\lim _{x \rightarrow 5^{+}} \frac{f(x)-f(a)}{x-a}

            =\lim _{x \rightarrow 5^{+}} \frac{\sqrt{x^{2}-10 x+25}-\sqrt{5^{2}-10(5)+25}}{x-5}

            \begin{aligned} &=\lim _{x \rightarrow 5^{+}} \frac{|x-5|}{x-5} \\\\ &=\lim _{x \rightarrow 5^{+}} \frac{x-5}{x-5} \\\\ &=1 \end{aligned}

L H D \neq R H D, so function is not differentiable .

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