https://file.aiquickdraw.com/mathbot/file/1727319997628xz2558k9.jpg

The question asks for the value of \( b \) in the definition of the derivative using the limit formula, given the function \( f(x) = 3x + 2 \). Let's break down the problem:

The derivative of \( f(x) \) at \( x = 2 \) is given by:

\[
f'(2) = \lim_{x \to 2} \frac{f(x) - f(2)}{x - 2}
\]

For \( f(x) = 3x + 2 \):

1. Calculate \( f(2) \):
\[
f(2) = 3(2) + 2 = 6 + 2 = 8
\]

So the expression becomes:
\[
f'(2) = \lim_{x \to 2} \frac{(3x + 2) - 8}{x - 2}
\]

This matches the form in the image where we have \( b = 8 \), since \( f(2) = 8 \).

Thus, \( b = 8 \).

The correct answer is **A. 8**.

---

Would you like further clarification? Here are some related questions to deepen your understanding:

1. What is the general definition of a derivative using limits?
2. How does one simplify limits of rational functions?
3. Why is the value \( b = 8 \) important in this particular case?
4. What is the geometric meaning of a derivative?
5. How does this process change for non-linear functions?

**Tip:** The derivative at a point gives the slope of the tangent line to the curve at that point.

Turunan dari f'(2) dari f(x) = 3x + 2 dengan menggunakan definisi turunan. Tentukan berapa nilai b?

Learn how to calculate the derivative of the linear function f(x) = 3x + 2 at x = 2 using the limit definition of the derivative. This solution provides a step-by-step breakdown of how to find the value of b and apply the derivative formula.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation