Question

Va rog sa ma ajutati!​

Answer 1

$f(x) = e^x-x-1\\f'(x) = e^x-1\\f'(x) = 0\Rightarrow e^x=1\Rightarrow x=0$

$\text{Din tabel, }\Rightarrow f\text{ este cresc\u atoare pe }[0, \infty).$

$\left. \begin{aligned} \sqrt{2009}, \sqrt{2010}\in[0,\infty)\\ \sqrt{2009}\leq\sqrt{2010}\\ f\text{ cresc\u atoare pe }[0, \infty) \end{aligned}\right\}\Rightarrow f(\sqrt{2009})\leq f(\sqrt{2010})\\\Leftrightarrow e^{\sqrt{2009}}-\sqrt{2009}-1\leq e^{\sqrt{2010}}-\sqrt{2010}-1\Leftrightarrow e^{\sqrt{2009}}+\sqrt{2010}\leq e^{\sqrt{2010}}+\sqrt{2009}$