Mathematics - Continuity - Differentiability Question with Solution | TestHub

Given,

$f\left(x\right)=\min \left\{x-\left[x\right],1+\left[x\right]-x\right\}$

So, the graph of the function is 

$1-\left\{x\right\}=1-x;0\le x<1$

From the graph we can say that the function is continuous at all points in the interval $\left[0,3\right].$

So, $P=0$

Again, from the diagram, we can say that at $x=\frac{1}{2},1,\frac{3}{2},2,\frac{5}{2},$ there are sharp edges.

So, the function is non differentiable at $x=\frac{1}{2},1,\frac{3}{2},2,\frac{5}{2}$

Hence, $Q=5$

So, $P+Q=5$