HMMT 2007 K4

Find the real number $\alpha$ such that the curve $f(x)=e^{x}$ is tangent to the curve $g(x)=\alpha x^{2}$ .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

e^{2} / 4

Solutions

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