grandes-ecoles 2018 Q30

grandes-ecoles · France · centrale-maths1__official Curve Sketching Variation Table and Monotonicity from Sign of Derivative

Show that for all $x \in [0, 1[$
$$\frac{x^{2}}{2} + (x - 1)\ln(1 - x) \leqslant \ln(2 + x) - \ln(2 - x)$$
One may perform a function study.

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

$$\frac{x^{2}}{2} + (x - 1)\ln(1 - x) \leqslant \ln(2 + x) - \ln(2 - x)$$

One may perform a function study.