Limit Continuity And Differentiability Ques 51
- Draw a graph of the function $ y=[x]+|1-x|,-1 \leq x \leq 3 . $
Determine the points if any, where this function is not differentiable.
(1989, 4M)
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Answer:
Correct Answer: 51.$\{0,1,2\}$
Solution: $y=[x]+|1-x|,-1 \leq x \leq 3$
$\begin{array}{ll}\Rightarrow & y= \begin{cases}-1+1-x, & -1 \leq x<0 \\ 0+1-x, & 0 \leq x<1 \\ 1+x-1, & 1 \leq x<2 \\ 2+x-1, & 2 \leq x \leq 3\end{cases} \\ \Rightarrow & y=\left\{\begin{array}{cc}-x, & -1 \leq x<0 \\ 1-x, & 0 \leq x<1 \\ +x, & 1 \leq x<2 \\ x+1, & 2 \leq x<3\end{array}\right.\end{array}$
which could be shown as,
Clearly, from above figure, $y$ is not continuous and not differentiable at $x=\{0,1,2\}$.
BETA
