The given function is:

\[
y = 5x^2 + \frac{2}{x^1/4}
\]

However, there seems to be a misrepresentation of the second term. Based on standard notation, I assume the expression is meant to be:

\[
y = 5x^2 + \frac{2}{4x}
\]

Or if you meant \(x^{-1/4}\), the correct expression would be:

\[
y = 5x^2 + 2x^{-1/4}
\]

Please confirm or clarify how you'd like the second term to be interpreted, and I can help further.

Would you like a detailed breakdown of any steps or results?

Here are 5 related questions:
1. How do you find the derivative of the function \(y = 5x^2 + 2x^{-1/4}\)?
2. How do you solve for the value of \(x\) when \(y = 0\) in this equation?
3. What is the behavior of the function as \(x \to 0\) or \(x \to \infty\)?
4. How does the presence of a negative fractional exponent affect the graph of the function?
5. How do you find the integral of \(5x^2 + 2x^{-1/4}\)?

**Tip:** When working with negative or fractional exponents, keep in mind the rules for differentiation and integration, as they can involve unique patterns.

Understand how to analyze and differentiate the function y = 5x^2 + 2x^-1/4, which involves fractional exponents. This problem includes detailed explanations of algebraic operations, differentiation, and integration, using the power rule. Suitable for high school and college-level students.

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