Question: In this exercise, you derive a bound on the largest absolute value of the derivative of a polynomial of a given order, in terms of

In this exercise, you derive a bound on the largest absolute value of the derivative of a polynomial of a given order, in terms of the size of the coefficients¹. For ω ∈ R^k+1, we define the polynomial p_ω, with values

Pw (x) = W + Wx + ... + Wk+1xk.

Show that, for any p ≥ 1

where ν = (ω₂, . . . ,ω_k+1) ∈ R^k, and

Pw (x) = W + Wx + ... + Wk+1xk.

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