The function provided in the image is:

$f(x) = \sqrt[3]{8 + x}, \quad x_0 = 0.$

Let me know how I can assist with this function. For example:

• Do you want the derivative $f'(x)$?
• Do you want the value of $f(0)$?
• Are you analyzing its properties or behavior near $x_0 = 0$?

Here are 5 questions you might explore next:

1. What is $f'(x)$ at $x_0 = 0$?
2. What is the behavior of $f(x)$ as $x \to \infty$?
3. Can the function $f(x)$ have any critical points?
4. What are the inflection points of $f(x)$?
5. Is $f(x)$ increasing or decreasing at $x_0 = 0$?

Tip: When working with cube roots, recall that their derivatives involve fractional powers, which can yield elegant simplifications.