Let f:` R to R and g:R to R` be respectively given by `f(x) =|x|+1 and g(x) =x^(2)+1)`. Define `h: R to R ` by
`h(x) ={{:( max{f(x) , g(x) },if xle0),(min{f(x) ,g(x) },if x gt 0):}`
then number of point at which h(x) is not differentiable is

Explanation

First we draw the graph, of `y= |x|+1 and y = x^(2) + 1`
`" "y = |x|+1 = {{:( x+1",",, x ge 0),( -x+1",",, xlt 0):}`
`y=x^(2)+1` is a parabola having vertex at (0, 1) and concave upwards
Thus, the graphs of both functions are as shown in the following figure.

From the graph, the required function is
`" "h(x) ={{:(x^(2)+1",",, x in (-oo, -1)), (-x+1",",, x in [-1, 0)), (x^(2)+1",",, x in [0, 1)), (x+1",",, x in [1, oo)):}`
which is non-different at `x=-1, 0 and 1`.