Putnam 1980 B1

For which real numbers $c$ is $\frac{e^x +e^{-x} }{2} \leq e^{c x^2 }$ for all real $x?$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.