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Evaluate the difference quotient for f (x) = -2x²-x+3 by completing the following steps: Make sure to simplify as much as possible at each step: 1. f (x + h) = 2. f (x+h)-f(x) = f (x + h). f(x+h)-f(x) h 3. 4. lim h→0 f(x+h)-f(x) h

Evaluate the difference quotient for f (x) = -2x²-x+3 by completing the following steps: Make sure to simplify as much as possible at each step: 1. f (x + h) = 2. f (x+h)-f(x) = f (x + h). f(x+h)-f(x) h 3. 4. lim h→0 f(x+h)-f(x) h

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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### Evaluate the Difference Quotient for \( f(x) = -2x^2 - x + 3 \) To evaluate the difference quotient for \( f(x) = -2x^2 - x + 3 \), follow these steps. Make sure to simplify as much as possible at each step: 1. **Calculate \( f(x + h) \)** \[ f(x + h) = \_\_\_\_\_\_ \] 2. **Compute \( f(x + h) - f(x) \)** \[ f(x + h) - f(x) = \_\_\_\_\_\_ \] 3. **Divide the result by \( h \)** \[ \frac{f(x + h) - f(x)}{h} = \_\_\_\_\_\_ \] 4. **Evaluate the limit as \( h \) approaches 0** \[ \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} = \_\_\_\_\_\_ \] Follow these steps precisely and simplify your expressions at each stage to determine the difference quotient accurately.
Transcribed Image Text:### Evaluate the Difference Quotient for \( f(x) = -2x^2 - x + 3 \) To evaluate the difference quotient for \( f(x) = -2x^2 - x + 3 \), follow these steps. Make sure to simplify as much as possible at each step: 1. **Calculate \( f(x + h) \)** \[ f(x + h) = \_\_\_\_\_\_ \] 2. **Compute \( f(x + h) - f(x) \)** \[ f(x + h) - f(x) = \_\_\_\_\_\_ \] 3. **Divide the result by \( h \)** \[ \frac{f(x + h) - f(x)}{h} = \_\_\_\_\_\_ \] 4. **Evaluate the limit as \( h \) approaches 0** \[ \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} = \_\_\_\_\_\_ \] Follow these steps precisely and simplify your expressions at each stage to determine the difference quotient accurately.
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