https://file.aiquickdraw.com/mathbot/file/17267035518947ytgyf9u.jpg

f prime left parenthesis x right parenthesisf′(x)equals=enter your response here

We are given the function \( f(x) = -8x + 4 \) and asked to find its derivative \( f'(x) \), and evaluate \( f'(2) \), \( f'(0) \), and \( f'(-6) \).

### Step 1: Find \( f'(x) \)
The function \( f(x) = -8x + 4 \) is a linear function, so its derivative is the slope of the function.

The derivative of \( f(x) = -8x + 4 \) is:
\[
f'(x) = \frac{d}{dx}(-8x + 4) = -8
\]

### Step 2: Evaluate \( f'(2) \), \( f'(0) \), and \( f'(-6) \)
Since \( f'(x) = -8 \), it remains constant for all values of \( x \). Therefore:

\[
f'(2) = -8
\]
\[
f'(0) = -8
\]
\[
f'(-6) = -8
\]

### Final Answer:
- \( f'(x) = -8 \)
- \( f'(2) = -8 \)
- \( f'(0) = -8 \)
- \( f'(-6) = -8 \)

Would you like further details or have any other questions?

Here are some related questions to explore:

1. What is the derivative of a constant function?
2. How does the derivative of a linear function compare to a quadratic function?
3. Can you explain why the derivative of a linear function is constant?
4. How would the derivative change if the function had a higher-degree term, such as \( x^2 \)?
5. What are the practical applications of finding derivatives of linear functions?

**Tip:** For linear functions, the derivative is always the slope of the line.

Find f'(x) for the following function. Then find f'(2), f'(0), and f'(-6). f(x) = -8x + 4

Learn how to find the derivative of the linear function f(x) = -8x + 4, and evaluate it at points x = 2, 0, and -6. This step-by-step guide covers key calculus concepts and derivative formulas, ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation