### Calculus Problem**Problem Statement**Consider the function $ g(x) = \frac{-2x + 3}{x + 1} $.#### Part 17a**Task:** Determine the slope function $ g'(x) $.**Solution:** \[ g'(x) = -\frac{5}{(x + 1)^2} \]_Solution is correct._#### Part 17b**Task:** Hence determine the slope at $ x = -2 $.**Solution:**\[ g'(-2) = -5 \]_Solution is correct._#### Part 17c**Task:** Determine the equation of the tangent to the curve $ g(x) $ at $ x = -2 $. Leave your answer in the form $ y = mx + b $.**Solution:**\[ y - g(-2) = g'(-2) \left( x - (-2) \right) \]_Solution is correct._**Note:** The final equation of the tangent line is yet to be determined (indicated by "???????"). The remaining steps are likely to involve simplifying the equation and substituting values for $ g(-2) $, $ g'(-2) $, and $ x $.### SummaryIn this exercise, we:1. Found the slope function $ g'(x) $ for a given rational function.2. Evaluated the slope of the function at a specific point.3. Set up the equation for the tangent line at this point.This step-by-step approach is an excellent example of applying calculus concepts to find tangent lines and understanding the properties of functions.

Name: ### Calculus Problem**Problem Statement**Consider the function $ g(x
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Description: ### Calculus Problem**Problem Statement**Consider the function \( g(x) = \frac{-2x + 3}{x + 1} $.#### Part 17a**Task:** Determine the slope function $ g'(x) $.**Solution:** \[ g'(x) = -\frac{5}{(x + 1)^2} \]_Solution is correct._#### Part 17b**Ta

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Answered: Consider the function g(x) = –2x+3 x +…

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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### Calculus Problem

**Problem Statement**

Consider the function $ g(x) = \frac{-2x + 3}{x + 1} $.

#### Part 17a

**Task:** Determine the slope function $ g'(x) $.

**Solution:**

\[ g'(x) = -\frac{5}{(x + 1)^2} \]

_Solution is correct._

#### Part 17b

**Task:** Hence determine the slope at $ x = -2 $.

**Solution:**

\[ g'(-2) = -5 \]

_Solution is correct._

#### Part 17c

**Task:** Determine the equation of the tangent to the curve $ g(x) $ at $ x = -2 $. Leave your answer in the form $ y = mx + b $.

**Solution:**

\[ y - g(-2) = g'(-2) \left( x - (-2) \right) \]

_Solution is correct._

**Note:** The final equation of the tangent line is yet to be determined (indicated by "???????"). The remaining steps are likely to involve simplifying the equation and substituting values for $ g(-2) $, $ g'(-2) $, and $ x $.

### Summary

In this exercise, we:
1. Found the slope function $ g'(x) $ for a given rational function.
2. Evaluated the slope of the function at a specific point.
3. Set up the equation for the tangent line at this point.

This step-by-step approach is an excellent example of applying calculus concepts to find tangent lines and understanding the properties of functions.

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