Exercise 3 (5 points). Let A: R x x R R be a multi-linear map...

   

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Exercise 3 (5 points). Let A: R" x x R → R be a multi-linear map with k entries. • Compute the differential of f(x) = A(x,...,x). • Prove that f € C¹ (R", R). • Prove that 0 € R" is a critical point of f if k> 1. • Prove that 0 € R" is a critical point of f, with k = 1, if and only if A = 0. Exercise 3 (5 points). Let A: R" x x R → R be a multi-linear map with k entries. • Compute the differential of f(x) = A(x,...,x). • Prove that f € C¹ (R", R). • Prove that 0 € R" is a critical point of f if k> 1. • Prove that 0 € R" is a critical point of f, with k = 1, if and only if A = 0.

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