Based on the information given, it should be noted that the LaGrange error bound will be E ≤ 4.
From the information given, it can be noted that the table below gives derivative values for the differentiable function f(x) whose derivatives are positive and increasing in value.
Therefore, the LaGrange error bound if we estimate the value of f(1) using a 4th degree polynomial will be:
= 6/4! (2 - 0)⁴
= 6/24 × 2⁴
= 1/4 × 16
= 4.
Therefore, the LaGrange error bound will be E ≤ 4.
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