I see that you've uploaded a set of questions asking to find the critical numbers of various functions. I'll walk through how to approach these types of problems:

General Approach:

To find the critical numbers of a function:

1. Differentiate the function to get its derivative.
2. Set the derivative equal to zero and solve for the variable. This will give you potential critical points.
3. Check for where the derivative does not exist (if applicable).
4. These solutions are the critical numbers of the function.

Now, let's break down each question individually.

Question 5:

Function: $g(y) = \frac{y - 3}{y^2 - 3y + 9}$

• Find the derivative $g'(y)$ using the quotient rule.
• Set $g'(y) = 0$ and solve for $y$.

Question 6:

Function: $p(x) = \frac{x^2 + 2}{2x - 1}$

• Use the quotient rule to differentiate.
• Set the derivative equal to zero to find critical points.

Question 7:

Function: $h(t) = t^{3/4} - 3t^{1/4}$

• Differentiate each term.
• Set the derivative equal to zero and solve for $t$.

Question 8:

Function: $F(x) = x^{4/5}(x - 4)^2$

• Apply the product rule to differentiate.
• Set the derivative equal to zero to find critical numbers.

Question 9:

Function: $g(x) = x^2 \ln(x)$

• Use the product rule to differentiate.
• Set the derivative equal to zero and solve for $x$.

Would you like detailed solutions for each of these steps?

Here are 5 relative questions:

1. What is the quotient rule for differentiation?
2. How do you handle non-differentiable points in critical number problems?
3. How do you differentiate functions involving natural logarithms?
4. Can a function have critical numbers where the derivative does not exist?
5. What role do second derivatives play in identifying local extrema?

Tip: Always check the domain of your function before finding critical numbers, as this can affect the solution.