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To find the slope of the tangent line to the curve described by the function \( f(x) = x^2 + x \) at the point where \( a = 1 \), we need to compute the derivative of \( f(x) \) and evaluate it at \( x = 1 \).

### Step 1: Find the derivative of \( f(x) \)
The derivative of a function gives the slope of the tangent line at any point \( x \). For \( f(x) = x^2 + x \), we apply the power rule to differentiate each term:

\[
f'(x) = \frac{d}{dx}(x^2) + \frac{d}{dx}(x)
\]

\[
f'(x) = 2x + 1
\]

### Step 2: Evaluate the derivative at \( x = 1 \)
To find the slope of the tangent line at \( x = 1 \), substitute \( x = 1 \) into the derivative:

\[
f'(1) = 2(1) + 1 = 2 + 1 = 3
\]

### Conclusion
The slope of the tangent line at \( x = 1 \) is \( \boxed{3} \).

Would you like further details or explanations? Here are some related questions you might find useful:

1. How do you find the equation of the tangent line at \( x = 1 \)?
2. What is the geometrical meaning of a derivative?
3. How does the power rule work for differentiation?
4. What happens to the slope of the tangent line for different values of \( x \)?
5. How do you find the second derivative of \( f(x) \)?

**Tip:** When finding the slope of a tangent line, always remember that the derivative at a specific point represents the slope at that point.

Find slope of the tangent line to the curve f(x) = x^2 + x, at the point where a = 1.

This page explains how to find the slope of the tangent line to the curve f(x) = x^2 + x at the point where x = 1. The solution uses the power rule for derivatives, with step-by-step instructions. Perfect for students in Grades 10-12 studying calculus.

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