Question: Let f: X Y be differentiable at x0 with derivative Df[x0], and let x be a vector of unit norm (||x|| = 1). Show that

Let f: X †’ Y be differentiable at x0 with derivative Df[x0], and let x be a vector of unit norm (||x|| = 1). Show that the directional derivative of f at x0 in the direction x is the value of the linear function Df[x0] at x, that is,

D,f[x] = Df[x](x)

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