Let `f:R-> R and g:R-> R` be respectively given by `f(x) = |x| +1 and g(x) = x^2 + 1`. Define `h:R-> R` by `h(x)={max{f(x), g(x)}, if xleq 0 and min{f(x), g(x)}, if x > 0`.The number of points at which `h(x)` is not differentiable is

Options

A. `1`
B. `2`
C. `3`
D. `4`

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`.