\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Derive AM-GM for \(n\) positive numbers from Jensen's inequality applied to \(\varphi = -\ln\). Specifically, show that for every \(x_1, \dots, x_n > 0\), $$ \frac{x_1 + \dots + x_n}{n} \ge (x_1 \cdots x_n)^{1/n}. $$
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.