(a) Use the results of Exercise 59 to prove that x^1/x = c has a unique solution if 0 < c ≤ 1 or c = e^1/e, has two solutions if 1 < c < e^1/e, and has no solutions if c > e^1/e.
(b) Plot the graph of ƒ(x) = x^1/x and verify that it confirms the conclusions of (a).

Data From Exercise 59

Let ƒ(x) = x^1/x for x > 0.