Find the value of the derivative of the function at the given point. 2 f(x) = 3x² − 4x; ( − 1,7) - f'( − 1) = □ (Type an integer or a simplified fraction.)
Find the value of the derivative of the function at the given point. 2 f(x) = 3x² − 4x; ( − 1,7) - f'( − 1) = □ (Type an integer or a simplified fraction.)
Chapter3: Functions
Section3.2: Domain And Range
Problem 2SE: How do we determine the domain of a function defined by an equation?
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![### Calculus Practice Problem: Derivative Evaluation
#### Problem Statement
Find the value of the derivative of the function at the given point.
\[ f(x) = 3x^2 - 4x; \quad (-1, 7) \]
\( f'(-1) = \) [Text Box] (Type an integer or a simplified fraction.)
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In this problem, you are asked to find the derivative of the function \( f(x) = 3x^2 - 4x \) and evaluate it at \( x = -1 \). Begin by differentiating the function:
1. **Differentiate the function**:
\[ f(x) = 3x^2 - 4x \]
\[ f'(x) = \frac{d}{dx}(3x^2 - 4x) \]
\[ f'(x) = 6x - 4 \]
2. **Evaluate the derivative at \( x = -1 \)**:
\[ f'(-1) = 6(-1) - 4 \]
\[ f'(-1) = -6 - 4 \]
\[ f'(-1) = -10 \]
Therefore, the value of the derivative at the given point is \( -10 \).
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Please enter \( -10 \) as your answer in the text box provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc944e8dc-d275-4b70-8def-6573a43e5eec%2F1961a22c-00d1-4695-a37e-4c4c2dd31241%2Fi1eluv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Practice Problem: Derivative Evaluation
#### Problem Statement
Find the value of the derivative of the function at the given point.
\[ f(x) = 3x^2 - 4x; \quad (-1, 7) \]
\( f'(-1) = \) [Text Box] (Type an integer or a simplified fraction.)
---
In this problem, you are asked to find the derivative of the function \( f(x) = 3x^2 - 4x \) and evaluate it at \( x = -1 \). Begin by differentiating the function:
1. **Differentiate the function**:
\[ f(x) = 3x^2 - 4x \]
\[ f'(x) = \frac{d}{dx}(3x^2 - 4x) \]
\[ f'(x) = 6x - 4 \]
2. **Evaluate the derivative at \( x = -1 \)**:
\[ f'(-1) = 6(-1) - 4 \]
\[ f'(-1) = -6 - 4 \]
\[ f'(-1) = -10 \]
Therefore, the value of the derivative at the given point is \( -10 \).
---
Please enter \( -10 \) as your answer in the text box provided.
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