If f x = Max 3 - x , 3 + x , 6 is not differentiable at x = a , and x = b , then a + b =

Plotting the diagram of the given function we have,

 

Now we see by diagram that maximum function is shaded by lines and between $x\equiv \left[-3,3\right]$ $y=6$ is maximum,

And we also know that in sharp corner function is non-differentiable,

So at $x=-3 \& x=3$ function is non-differentiable,

So, $\left|-3\right|+\left|3\right|=6$