If h(x) 0 for x 0 and h(x) 1 for x 0, prove there does not exist a function f R R such that f(x) h(x) for all x R Give examples of two functions, not differing by a constant, whose derivatives equal h(x) for all x 0

Question: If h(x) := 0 for x < 0 and h(x) := 1 for x > 0, prove there does not exist a function f :

If h(x) := 0 for x < 0 and h(x) := 1 for x > 0, prove there does not exist a function f : R → R such that fʹ(x) = h(x) for all x ∈ R. Give examples of two functions, not differing by a constant, whose derivatives equal h(x) for all x ≠ 0.

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