### 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
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
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