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Homework Statement
Let f(x) = x^3+ ax^2+ bx + c with a, b, c real. Show that
M = max|f(x)|≥1/4
-1 ≤ x ≤ 1
and find all cases where equality occurs.
Homework Equations
The Attempt at a Solution
|(-1 ≤ x^3 ≤ 1)+(-a ≤ ax^2 ≤ a)+(-b ≤ bx ≤ b)+c|≥1/4?
not sure how to prove without knowing what a,b,c are?