MathDB

19

Part of 2019 BMT Spring

Problems(1)

2019 BMT Individual 19

Source:

1/9/2022
Let aa and bb be real numbers such that max⁡0≤x≤1∣x3−ax−b∣\max_{0\le x\le 1} |x^3 - ax - b| is as small as possible. Find a+ba + b in simplest radical form.
(Hint: If f(x)=x3−cx−df(x) = x^3 - cx - d, then the maximum (or minimum) of f(x)f(x) either occurs when x=0x = 0 and/or x=1x = 1 and/or when x satisfies 3x2−c=03x^2 - c = 0).
algebra