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To find the slope of the function's graph at the given point \((-3, 3)\) for the function \( f(x) = 2x^2 + 5x \), we need to calculate the derivative of \( f(x) \) and then evaluate it at \( x = -3 \).

### Step 1: Find the derivative
The derivative of \( f(x) = 2x^2 + 5x \) with respect to \( x \) is:
\[
f'(x) = \frac{d}{dx}(2x^2 + 5x)
\]
Using the power rule for differentiation:
\[
f'(x) = 4x + 5
\]

### Step 2: Evaluate the derivative at \( x = -3 \)
Now, substitute \( x = -3 \) into \( f'(x) \):
\[
f'(-3) = 4(-3) + 5 = -12 + 5 = -7
\]

### Conclusion
The slope of the function at the point \( (-3, 3) \) is \( \boxed{-7} \).

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What is the geometric interpretation of a negative slope?
2. How would you find the equation of the tangent line at \( x = -3 \)?
3. What is the second derivative of \( f(x) = 2x^2 + 5x \) and what does it tell us?
4. How does the slope of a quadratic function change as \( x \) increases or decreases?
5. What are the critical points of \( f(x) = 2x^2 + 5x \), and how do we find them?

**Tip:** When differentiating polynomial functions, the power rule \(\frac{d}{dx} x^n = nx^{n-1}\) is your go-to method for quick and accurate results.

Find the slope of the function's graph at the given point: f(x) = 2x^2 + 5x, (-3, 3).

Learn how to find the slope of the function f(x) = 2x^2 + 5x at the point (-3, 3). This problem involves differentiation and uses the power rule to find the slope of a quadratic function. Suitable for students in Grades 9-12.

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