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The image contains a mathematical problem that reads:

**"Persamaan garis \( f(x) = 3x + 4 \) didiferensiasi terhadap garis \( y = -4 \). Tentukan nilai \( f'(3) \)!"**

This is asking for the derivative of the linear function \( f(x) = 3x + 4 \) and to evaluate that derivative at \( x = 3 \).

### Solution:

1. The function given is \( f(x) = 3x + 4 \).
2. To differentiate this function with respect to \( x \), we use the basic rule of differentiation for polynomials:
   \[
   f'(x) = \frac{d}{dx}(3x + 4)
   \]
   The derivative of \( 3x \) is 3 (since the derivative of \( x^n \) is \( nx^{n-1} \), and here \( n = 1 \)), and the derivative of the constant \( 4 \) is 0. Therefore:
   \[
   f'(x) = 3
   \]
3. Now, we evaluate \( f'(3) \):
   \[
   f'(3) = 3
   \]
   
Thus, the value of \( f'(3) \) is **3**.

Do you need further clarification or have any additional questions?

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Here are some related questions that expand on this topic:

1. What is the geometric interpretation of the derivative of a function?
2. How do you differentiate more complex functions, such as products or quotients of functions?
3. What is the physical meaning of the derivative in real-world problems?
4. How does the concept of the slope of a line relate to the derivative?
5. How would you find the second derivative of the given function \( f(x) = 3x + 4 \)?

**Tip:** For linear functions like \( f(x) = ax + b \), the derivative is always the slope \( a \), because the rate of change is constant.

Persamaan garis f(x) = 3x + 4 didiferensiasi terhadap garis y = -4. Tentukan nilai f'(3)!

Find the derivative of the linear function f(x) = 3x + 4 and calculate f'(3). This problem covers key calculus concepts like differentiation and is suitable for Grades 10-12.

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