## Irrational Exponentiation

What is greater, or ?

Consider a function and check if it’s greater than 1 at .

It’s easy to see that , but we want to know which way the function goes from there.

which is positive for all . So this function goes up when . We know that , therefore and .

wxMaxima plot:

```
plot2d(%e^x/x^%e,[x,2.5,3.5],[ylabel,"f(x)"]);
```