grandes-ecoles 2018 Q31

grandes-ecoles · France · centrale-maths1__mp Curve Sketching Number of Solutions / Roots via Curve Analysis

Deduce that for all $x \in [0, 1[$
$$1 + \exp\left(\frac{x^{2}}{2}\right)(1 - x)^{x - 1} \leqslant \frac{4}{2 - x}$$

Deduce that for all $x \in [0, 1[$

$$1 + \exp\left(\frac{x^{2}}{2}\right)(1 - x)^{x - 1} \leqslant \frac{4}{2 - x}$$