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The problem asks to determine the value of \( f(2) + f'(1) \) based on the graph of the function \( f \).

### Step 1: Find \( f(2) \)
From the graph, locate \( x = 2 \). The value of the function \( f(2) \) is the \( y \)-coordinate of the point where \( x = 2 \). From the graph, it seems that at \( x = 2 \), \( f(2) = 4 \).

### Step 2: Find \( f'(1) \)
\( f'(1) \) represents the derivative of the function at \( x = 1 \), which is the slope of the tangent line to the graph at that point. At \( x = 1 \), the tangent line appears to be horizontal, indicating that the slope is zero. Therefore, \( f'(1) = 0 \).

### Step 3: Calculate \( f(2) + f'(1) \)
Now, we add the values:
\[
f(2) + f'(1) = 4 + 0 = 4
\]
However, this value does not correspond to any of the answer choices. Let's recheck the derivative at \( x = 1 \). Looking again at the graph, it's possible that the slope is slightly negative, giving a different result.

Given this ambiguity in the derivative, it might be better to reconsider the slope at \( x = 1 \) more carefully or obtain a clearer image. Would you like further clarification on this, or should we try to fine-tune the details based on the graph?

Also, here are 5 related questions for further practice:
1. How do you estimate the slope of a tangent line at a given point on a graph?
2. What are the steps to calculate a derivative at a specific point graphically?
3. How can we determine critical points using the first derivative?
4. What is the significance of a zero slope in the context of a function’s graph?
5. How do you interpret the second derivative from a graph?

**Tip:** Always check for changes in the slope around points of interest, especially if it seems unclear or near-zero.

A partir de la gráfica de la función f mostrada en la figura, ¿cuál es el valor de f(2) + f'(1)?

Determine the value of f(2) and f'(1) from the graph of the function. Learn how to read function values and estimate derivatives using tangent lines. Suitable for Grades 10-12.

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