Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![The task is to find the derivative of the function \( f(x) = 2x^2 - 5x + 2 \) at a specific point \( a \).
Given:
\[ f(x) = 2x^2 - 5x + 2 \]
To find:
\[ f'(a) = \]
A blank box is provided for the answer, followed by a red cross, indicating an incorrect or incomplete attempt.
**Solution Explanation:**
To find the derivative \( f'(x) \), apply the power rule:
1. Differentiate \( 2x^2 \) to get \( 4x \).
2. Differentiate \(-5x\) to get \(-5\).
3. The derivative of the constant \(2\) is \(0\).
Thus, the derivative is:
\[ f'(x) = 4x - 5 \]
To find \( f'(a) \), substitute \( a \) for \( x \) in the derivative:
\[ f'(a) = 4a - 5 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe28b8fdf-2552-4f73-8b1c-90734de9299b%2F270cd98a-3635-4f6c-94c2-f6adf9b81a7b%2F6n6okxh_processed.png&w=3840&q=75)
Transcribed Image Text:The task is to find the derivative of the function \( f(x) = 2x^2 - 5x + 2 \) at a specific point \( a \).
Given:
\[ f(x) = 2x^2 - 5x + 2 \]
To find:
\[ f'(a) = \]
A blank box is provided for the answer, followed by a red cross, indicating an incorrect or incomplete attempt.
**Solution Explanation:**
To find the derivative \( f'(x) \), apply the power rule:
1. Differentiate \( 2x^2 \) to get \( 4x \).
2. Differentiate \(-5x\) to get \(-5\).
3. The derivative of the constant \(2\) is \(0\).
Thus, the derivative is:
\[ f'(x) = 4x - 5 \]
To find \( f'(a) \), substitute \( a \) for \( x \) in the derivative:
\[ f'(a) = 4a - 5 \]
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