Find x and y of critical pt

For any constant a, a family of functions is given by the following for x > 0.
y(x) = ax - x ln x

(a) What is the x-intercept of the graph of f(x)?

(b) Find the coordinates of the critical point.

(c) Classify the critical point as a maximum, minimum, or neither.

I found part (a) by setting whole function as 0.
And I got x = e^a