https://file.aiquickdraw.com/mathbot/file/1726597206537h8wszc77.jpg

The function shown in the image is:

\[
f(x) = \frac{x^2}{\sqrt{6 - x}}
\]

Would you like help finding the domain, derivative, or any other property of this function?

Here are five related questions:
1. What is the domain of the function \( f(x) = \frac{x^2}{\sqrt{6 - x}} \)?
2. How do you find the derivative of \( f(x) = \frac{x^2}{\sqrt{6 - x}} \)?
3. Can you simplify the expression \( f(x) = \frac{x^2}{\sqrt{6 - x}} \) further?
4. What happens to \( f(x) \) as \( x \) approaches 6?
5. What are the critical points of \( f(x) = \frac{x^2}{\sqrt{6 - x}} \)?

**Tip:** When working with functions that have square roots in the denominator, always consider the restrictions on the domain based on what values make the denominator zero or undefined.

What is the function f(x) = x^2 / sqrt(6 - x)?

Explore the function f(x) = x^2 / sqrt(6 - x), focusing on determining its domain, finding its derivative, and understanding key mathematical concepts involving square roots and rational functions. Suitable for advanced high school students.

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