Question: Let f: Rn R. Suppose that for each unit vector u Rn, the directional derivative Duf(a + tu) exists for t [0,

Let f: Rn → R. Suppose that for each unit vector u ∈ Rn, the directional derivative Duf(a + tu) exists for t ∈ [0, 1 ] (see Definition 11.19). Prove that
f(a + u) - f(a) = Duf(a + tu)
for some t ∈ (0, 1).

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