What value of x 0 maximizes ? (Enter a decimal.)

HardCalculus & Linear AlgebraAcceptance 51%

Maximize x^(1/x)

Jane StreetSIG / Susquehanna

What value of x > 0 maximizes $x^{1/x}$ ? (Enter a decimal.)

Approach

Take logs first, then differentiate $\frac{\ln x}{x}$ .

The answer is a famous constant.

Answer

Show the final answer

The answer is 2.71828. Sign in free for the full worked solution and to check your own answer.