**Problem Statement** Find the equation(s) of the tangent line(s) to the graph of the indicated equation at the point(s) with the given value of \( x \). \[ xy - 10x + 8 = 0; \, x = 2 \] **Instructions** Find the equation(s) of the tangent line(s) to the graph of the given equation at \( x = 2 \). (Type an equation. Use a comma to separate answers as needed.) --- In this problem, you are asked to find the tangent line(s) to the curve described by the equation \( xy - 10x + 8 = 0 \) at the specific value of \( x = 2 \). To solve this, you first need to identify the points on the curve where \( x = 2 \). Then, determine the derivative of the equation to find the slope of the tangent at those points, and use the point-slope form to find the actual equation of the tangent line(s).

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...
Question
**Problem Statement**

Find the equation(s) of the tangent line(s) to the graph of the indicated equation at the point(s) with the given value of \( x \).

\[ xy - 10x + 8 = 0; \, x = 2 \]

**Instructions**

Find the equation(s) of the tangent line(s) to the graph of the given equation at \( x = 2 \).

(Type an equation. Use a comma to separate answers as needed.) 

---

In this problem, you are asked to find the tangent line(s) to the curve described by the equation \( xy - 10x + 8 = 0 \) at the specific value of \( x = 2 \). To solve this, you first need to identify the points on the curve where \( x = 2 \). Then, determine the derivative of the equation to find the slope of the tangent at those points, and use the point-slope form to find the actual equation of the tangent line(s).
Transcribed Image Text:**Problem Statement** Find the equation(s) of the tangent line(s) to the graph of the indicated equation at the point(s) with the given value of \( x \). \[ xy - 10x + 8 = 0; \, x = 2 \] **Instructions** Find the equation(s) of the tangent line(s) to the graph of the given equation at \( x = 2 \). (Type an equation. Use a comma to separate answers as needed.) --- In this problem, you are asked to find the tangent line(s) to the curve described by the equation \( xy - 10x + 8 = 0 \) at the specific value of \( x = 2 \). To solve this, you first need to identify the points on the curve where \( x = 2 \). Then, determine the derivative of the equation to find the slope of the tangent at those points, and use the point-slope form to find the actual equation of the tangent line(s).
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