Estimating the Best Coefficient

★ 8/10calculus Taylor Series Estimation inequality Discriminant

Problem

Suppose that for every $x \in [0, 1]$ ,

\mathrm{e}^x + ax^3 - ax^2 - 1 \geqslant 0.

Let $\mu$ be the maximum possible value of the real number $a$ . Prove that

5 < \mu < \frac{26}{5}.

Answer

Solution

Difficulty	8/10
Topics	calculus, Taylor Series, Estimation, inequality, Discriminant

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