I've just encountered the following exercise from GEOFFREY A. JEHLE micro's book
Strict monotonicity comes from the fact that any increase in $x_1$ or $x_2$ increases utility, and strict convexity comes from the fact that a convex combination of any pair of bundles is strictly preferred to the pair. However, in this example, we can go in the situation where we get Leontief preferences ($\rho \to - \infty$). In that case prefences are weakly monotone and weakly convex. Why preferences can be easily verified to be strictly monotonic and strictly convex? Also, could you provide an example showing how to prove that the CES utility function has strict convex preferences?