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  • Need solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Fill in the blanks question 11

Need solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Fill in the blanks question  11

Answers (1)

Answer: x=2

Hint:

Given: f(x)=\left\{\begin{array}{l} x+1, x<2 \\ 2 x-1, x \geq 2 \end{array}\right\}

Solution:  

\begin{aligned} &L f(x)=x+1 \\ &f^{\prime}(x)=1 \\ &f(1)=1+1=2 \end{aligned}                            \begin{aligned} &R f(x)=2 x-1 \\ &f^{\prime}(x)=2 \\ &f(1)=2-1=1 \end{aligned}

f(2)=2+1=3                            f(2)=2(2)-1=4-1=3

\therefore L f(x)=R f(x)

Hence, f(x)=\left\{\begin{array}{l} x+1, x<2 \\ 2 x-1, x \geq 2 \end{array}\right\} is not differentiable at x=2. 

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