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You've uploaded an image containing five different functions. I'll list them here and can help you analyze or differentiate any of them:

1. \( f(x) = x^7 + 10 \)
2. \( f(x) = 5x^3 - x + 1 \)
3. \( f(x) = 4x^2 - 7x \)
4. \( f(x) = 8x^4 + 9x^2 - 1 \)
5. \( f(x) = x^4 + \frac{2}{x} \)

Let me know how you'd like to proceed. For example, I can:

- Differentiate these functions.
- Evaluate them for specific values of \( x \).
- Analyze their critical points or behavior.

Would you like details on one of these options or something else?

Here are five questions you might explore based on this content:
1. What is the derivative of each function?
2. What are the critical points of \( f(x) = x^4 + \frac{2}{x} \)?
3. What is the degree of the polynomial in each function?
4. What are the inflection points of \( f(x) = 8x^4 + 9x^2 - 1 \)?
5. How does the graph of \( f(x) = 5x^3 - x + 1 \) behave for large \( |x| \)?

**Tip:** When differentiating functions with fractions, use the quotient rule carefully to handle terms like \( \frac{2}{x} \).

Analyze the following functions:
1. f(x) = x^7 + 10
2. f(x) = 5x^3 - x + 1
3. f(x) = 4x^2 - 7x
4. f(x) = 8x^4 + 9x^2 - 1
5. f(x) = x^4 + 2/x

Explore the analysis of various polynomial and rational functions, including finding derivatives, critical points, and behavior for functions such as f(x) = x^7 + 10 and f(x) = x^4 + 2/x. This is suitable for students at Grades 11-12 or early college level.

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