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

Show that, for any p ≥ 1

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

Transcribed Image Text:

Pw (x) = W₁ + W₂x + ... + Wk+1xk.