To find the derivative of the function \( f(x) = x^3 - 3x + 4 \), we apply the rules of differentiation:

1. The derivative of \( x^n \) is \( nx^{n-1} \).
2. The derivative of a constant is 0.

Now, let's differentiate each term:

\[
f'(x) = \frac{d}{dx}(x^3) - \frac{d}{dx}(3x) + \frac{d}{dx}(4)
\]

Calculating the derivatives:

1. \( \frac{d}{dx}(x^3) = 3x^2 \)
2. \( \frac{d}{dx}(3x) = 3 \)
3. \( \frac{d}{dx}(4) = 0 \)

Combining these, we get:

\[
f'(x) = 3x^2 - 3
\]

### Therefore, the derivative of \( f(x) = x^3 - 3x + 4 \) is:

\[
f'(x) = 3x^2 - 3
\]

Would you like a more detailed explanation or have any questions?

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Here are some related questions you might find useful:

1. How do you find the derivative of a polynomial function in general?
2. What is the second derivative of \( f(x) = x^3 - 3x + 4 \)?
3. How does the derivative \( f'(x) \) help determine the critical points of \( f(x) \)?
4. How can you find the local maximum and minimum points using derivatives?
5. What are the applications of derivatives in real-world scenarios?

**Tip:** Remember that the derivative of a function gives the slope of the tangent line at any point on the function's curve.

Learn how to find the derivative of the function f(x) = x^3 - 3x + 4 using basic differentiation rules. This guide covers key calculus concepts, including the power rule and the differentiation of polynomials, suitable for high school students in Grades 11-12.

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