Question

4) For each of the following functions, establish on which subset of its domain it is C1. (You do not need to provide formal proofs in your answers: an explanation or brief graphical argument is sufficient.) Compute partial derivatives for these subsets.

(a) f(x) = ⌈x⌉ (recall ⌈x⌉ is the lowest integer above or equal to x).

(b) f(x, y) = min{x, y}.

(c) f(x, y) = xαyβ where α, β ∈ (0,1).

Answer 1