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The problem is asking for the equation of the tangent line to the function \( f(x) = x^2 + x \) at the point \( (1, 2) \), and it provides the derivative \( f'(x) = 2x + 1 \).

### Step-by-Step Solution:

1. **Equation of a Tangent Line:**
   The general form for the equation of the tangent line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( m \) is the slope of the tangent line, and \( (x_1, y_1) \) is the point of tangency.

2. **Slope of the Tangent Line:**
   The slope of the tangent line at a given point is the derivative of the function at that point. The derivative is provided as \( f'(x) = 2x + 1 \).

   To find the slope at \( x = 1 \):
   \[
   f'(1) = 2(1) + 1 = 3
   \]
   So, the slope \( m = 3 \).

3. **Point of Tangency:**
   The point of tangency is given as \( (1, 2) \).

4. **Substitute into the Tangent Line Equation:**
   Using the point \( (1, 2) \) and the slope \( m = 3 \) in the equation of the line:
   \[
   y - 2 = 3(x - 1)
   \]
   Simplifying this:
   \[
   y - 2 = 3x - 3
   \]
   \[
   y = 3x - 1
   \]

### Final Answer:
The equation of the tangent line is \( y = 3x - 1 \).

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Would you like more details on any step? Here are some related questions:

1. What is the geometric meaning of a tangent line?
2. How do you find the derivative of a function like \( f(x) = x^2 + x \)?
3. Can you explain how the point-slope form works in different situations?
4. How would you find the tangent line if the derivative wasn't given?
5. What happens when the slope at a point is zero?

**Tip:** Remember, the slope of the tangent line is equal to the value of the derivative at the point of interest.

Which of the following is the equation for the tangent line to f(x) = x^2 + x at the point (1, 2)? Note that f'(x) = 2x + 1.

This problem explains how to find the equation of a tangent line to the function f(x) = x^2 + x at the point (1, 2). Using the given derivative f'(x) = 2x + 1, the solution covers how to calculate the slope and apply it to the tangent line equation. Suitable for high school calculus students.

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