Question

The function $y=[x]+|1-x|,-1\le x\le 3$ Then $f(x)$ is not differentiable at (where [ $\cdot$ represents greatest integer function)

• A. two points
• B. three points
• C. four points
• D. five points

Answer 1

Answer: (C)

We have $y=[x]+|1-x|,-1\le x\le 3$
or $y=\{\begin{array}{ll}-1+1-x,& \text{ −1≤x<0}\\ 0+1-x,& \text{ 1≤x<1 }\\ -1-1+x,& \text{ 1≤x<2}\\ 2-1+x,& \text{ 2≤x<3}\\ 3-1+x,& \text{ x=3}\end{array}$
or $y=\{\begin{array}{ll}-x,& \text{ −1≤x<0}\\ 1-x,& \text{ 0≤x<1 }\\ x,& \text{ 1≤x<2}\\ 1+x,& \text{ 2≤x<2}\\ 5,& \text{ x=3}\end{array}$
Clearly, $f(x)$ is discontinuous at x = 0,1, 2, 3 and hence non-differentiable