F(x)=x3+5x F(x)=5x3 F(x)=13x2+26

It looks like you’ve provided three different expressions, presumably for the same variable \( x \). Let's clarify and analyze them one by one: 1. **\( f(x) = x^3 + 5x \)**: This is a polynomial function. You can analyze its characteristics such as roots, derivative, etc. 2. **\( F(x) = 5x^3 \)**: This is also a polynomial function. If this is related to \( f(x) \), you could be looking for the relationship in terms of derivatives or integrals. 3. **\( F(x) = 13x^2 + 26 \)**: This appears to be another expression for \( F(x) \). However, it seems inconsistent to have two different expressions for \( F(x) \) unless you meant different functions altogether. ### Possible Interpretations: - If you want to find the derivative of \( f(x) \), you can do so: \[ f'(x) = \frac{d}{dx}(x^3 + 5x) = 3x^2 + 5 \] - If you want to set \( F(x) = 5x^3 \) equal to \( F(x) = 13x^2 + 26 \), you can equate them: \[ 5x^3 = 13x^2 + 26 \] This polynomial equation can be solved for \( x \). - If you are looking for the integral of \( f(x) \), it would be: \[ \int f(x) \, dx = \int (x^3 + 5x) \, dx = \frac{x^4}{4} + \frac{5x^2}{2} + C \] where \( C \) is the constant of integration. Please clarify what you would like to do with these functions, and I would be happy to assist!