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Let's solve the derivative of the function provided in the images.

The function is:

\[
y = x^3 - 11x^2 + 24x + 4
\]

To find the derivative \(\frac{dy}{dx}\), we will apply the power rule to each term. The power rule states that if \(y = ax^n\), then \(\frac{dy}{dx} = nax^{n-1}\).

1. For \(x^3\): The derivative is \(3x^2\).
2. For \(-11x^2\): The derivative is \(-22x\).
3. For \(24x\): The derivative is \(24\).
4. For the constant \(4\): The derivative is \(0\) (since the derivative of a constant is 0).

Now, summing all these results:

\[
\frac{dy}{dx} = 3x^2 - 22x + 24
\]

This is the derivative of the function.

Would you like more details or have any questions?

Here are five related questions:
1. What is the second derivative of the function?
2. How can the derivative be used to find critical points?
3. How does the derivative relate to the slope of the function at a given point?
4. What are the steps for applying the product rule or quotient rule?
5. How do we interpret the derivative in real-world applications, like velocity?

**Tip**: Always simplify the derivative step-by-step for each term to avoid mistakes when differentiating complex functions.

Find the derivative of the function y = x^3 - 11x^2 + 24x + 4

Learn how to find the derivative of the function y = x^3 - 11x^2 + 24x + 4 using the power rule. This problem focuses on applying the power rule to differentiate each term step-by-step. Suitable for students in Grades 11-12.

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