Calculus › Extrema and curve sketching › Bounds from derivatives

Smallest bound on derivative at zero

High school · ●●●○○ 50 pts

Find the smallest real number AA such that for every quadratic polynomial f(x)f(x) satisfying ∣f(x)∣⩽1|f(x)| \leqslant 1 for all 0⩽x⩽10 \leqslant x \leqslant 1, the inequality f′(0)⩽Af'(0) \leqslant A holds.

Sign in to save your progress.

quadratic functionsderivativesoptimizationChebyshev polynomialsinequalities