Let f (x) = 2 for x (a) Prove that there does not exist a function F such that F ′(x) = f (x) for all x ∈ R. (b) Find examples of two functions g and h, not differing by a constant, such that g ′(x)...

Let f (x) = 2 for x <>

(a) Prove that there does not exist a function F such that F ′(x) = f (x) for all x ∈ R.

(b) Find examples of two functions g and h, not differing by a constant, such that g ′(x) = h ′(x) = f (x) for all x ≠ 0.