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

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

Solution:

  1. The function given is f(x)=3x+4f(x) = 3x + 4.
  2. To differentiate this function with respect to xx, we use the basic rule of differentiation for polynomials: f(x)=ddx(3x+4)f'(x) = \frac{d}{dx}(3x + 4) The derivative of 3x3x is 3 (since the derivative of xnx^n is nxn1nx^{n-1}, and here n=1n = 1), and the derivative of the constant 44 is 0. Therefore: f(x)=3f'(x) = 3
  3. Now, we evaluate f(3)f'(3): f(3)=3f'(3) = 3

Thus, the value of f(3)f'(3) is 3.

Do you need further clarification or have any additional questions?


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+4f(x) = 3x + 4?

Tip: For linear functions like f(x)=ax+bf(x) = ax + b, the derivative is always the slope aa, 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