Question

Let f:R → R and g:R → R be respectively given by f(x) = |x| + 1 and g(x) = x2 + 1. Define h:R → R by

h(x) = {(max {f(x), g(x)} : x ≤ 0), (min{f(x), g(x)} : x > 0)

Then the number of points at which h (x) is not differentiable is...

Answer 1

Clearly f(x) is not differentiable at x = – 1, 0, 1.

Thus, the number of points non-differentiable points = 3.