Chapter 4.5, Problem 64E

To determine

(a)

To show:

That $x^{\frac{1}{x}}=c$ has a unique solution of $0\le c\le 1$ or $c=e^{\frac{1}{e}}$, two solutions for $1<c<e^{\frac{1}{e}}$ and no solution for $c>e^{\frac{1}{e}}$.

To determine

(b)

To graph:

The function $f\left(x\right)=x^{\frac{1}{x}}$.