Math Problem Statement
jawaban
Persamaan garis f(x) = 3x + 4 didiferensiasi terhadap garis y = -4. Tentukan nilai f'(3)!
Solution
The image contains a mathematical problem that reads:
"Persamaan garis didiferensiasi terhadap garis . Tentukan nilai !"
This is asking for the derivative of the linear function and to evaluate that derivative at .
Solution:
- The function given is .
- To differentiate this function with respect to , we use the basic rule of differentiation for polynomials: The derivative of is 3 (since the derivative of is , and here ), and the derivative of the constant is 0. Therefore:
- Now, we evaluate :
Thus, the value of is 3.
Do you need further clarification or have any additional questions?
Here are some related questions that expand on this topic:
- What is the geometric interpretation of the derivative of a function?
- How do you differentiate more complex functions, such as products or quotients of functions?
- What is the physical meaning of the derivative in real-world problems?
- How does the concept of the slope of a line relate to the derivative?
- How would you find the second derivative of the given function ?
Tip: For linear functions like , the derivative is always the slope , because the rate of change is constant.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Linear Functions
Formulas
f'(x) = 3
Theorems
Derivative of a linear function
Suitable Grade Level
Grades 10-12