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3 of the If f(x) = , find f'(3), using the definition of derivative. f'(3) is the limit as x → expression ((1/x^2)- The value of this limit is -2*3^-3

3 of the If f(x) = , find f'(3), using the definition of derivative. f'(3) is the limit as x → expression ((1/x^2)- The value of this limit is -2*3^-3

Calculus: Early Transcendentals
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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**Problem Statement:** If \( f(x) = \frac{1}{x^2} \), find \( f'(3) \) using the definition of derivative. **Solution Approach:** The derivative \( f'(3) \) is the limit as \( x \to 3 \) of the expression: \[ \frac{\left(\frac{1}{x^2}\right) - \left(\frac{1}{3^2}\right)}{x - 3} \] **Solution:** The value of this limit is \( -2 \cdot 3^{-3} \).
Transcribed Image Text:**Problem Statement:** If \( f(x) = \frac{1}{x^2} \), find \( f'(3) \) using the definition of derivative. **Solution Approach:** The derivative \( f'(3) \) is the limit as \( x \to 3 \) of the expression: \[ \frac{\left(\frac{1}{x^2}\right) - \left(\frac{1}{3^2}\right)}{x - 3} \] **Solution:** The value of this limit is \( -2 \cdot 3^{-3} \).
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