I have opened the image you uploaded. Let me now extract the answers to the questions presented in the image.

1. For $f(x) = x^3 + 9x^2 - 81x$, the critical numbers are:
   x = 0, -9, 3

2. For $g(y) = \frac{y - 5}{y^2 - 3y + 15}$, the critical numbers are:
   y = DNE (since there are no real critical points)

3. For $h(p) = \frac{p - 1}{p^2 + 7}$, the critical numbers are:
   p = 1

Let me know if you'd like to go over the solutions in detail or have any questions!

Here are five follow-up questions related to these concepts:

1. How do you find the critical numbers for any function?
2. What does it mean when a function has no critical points?
3. How does the first derivative help in identifying critical numbers?
4. What is the significance of critical numbers in determining local extrema?
5. How do rational functions differ in terms of finding critical points compared to polynomial functions?

Tip: Always check if a function is undefined at certain points when working with rational functions.