Find the equation of the tangent line to the graph of the given equation at the indicated point. x?y2 + 4xy = 12, (2, 1) Use a calculator or computer software to graph the function and the tangent line. y 6. 191 9.
Find the equation of the tangent line to the graph of the given equation at the indicated point. x?y2 + 4xy = 12, (2, 1) Use a calculator or computer software to graph the function and the tangent line. y 6. 191 9.
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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![**Find the equation of the tangent line to the graph of the given equation at the indicated point.**
Given equation:
\[ x^2y^2 + 4xy = 12 \]
Indicated point: \( (2, 1) \)
**Graphical Representations:**
Three separate graphs are shown, each depicting the curve described by the equation \( x^2y^2 + 4xy = 12 \), along with a plotted tangent line. The graphs aim to help visualize how the tangent line interacts with the hyperbola-like curve. Each graph contains an axis labeled \( x \) and \( y \), ranging from -10 to 10 on both axes.
1. **First graph:**
- Displays the curve and a horizontal tangent line intersecting the curve.
2. **Second graph:**
- Shows the curve with an upward-sloping tangent line crossing the curve at the learned point. This might represent a more accurate tangent determiner depending on the slope calculation.
3. **Third graph:**
- Features a downward-sloping tangent line interacting with the curve.
Each graph includes a small circle below it, likely intended for selection to identify which graph correctly visualizes the tangent line with respect to the curve's behavior at the point \( (2, 1) \).
**Instructions:**
Use a calculator or computer software to graph the function and correctly identify the tangent line through calculation.
This exercise intends to enhance understanding of differentiating curves and finding tangent lines by checking which graphical representation aligns with the theoretical calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8184eabc-db64-4ff4-8675-5dfdbf4594d7%2Fb9e7c83a-68f5-4d82-9e8e-903dc20ec743%2F0vgfqox_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the equation of the tangent line to the graph of the given equation at the indicated point.**
Given equation:
\[ x^2y^2 + 4xy = 12 \]
Indicated point: \( (2, 1) \)
**Graphical Representations:**
Three separate graphs are shown, each depicting the curve described by the equation \( x^2y^2 + 4xy = 12 \), along with a plotted tangent line. The graphs aim to help visualize how the tangent line interacts with the hyperbola-like curve. Each graph contains an axis labeled \( x \) and \( y \), ranging from -10 to 10 on both axes.
1. **First graph:**
- Displays the curve and a horizontal tangent line intersecting the curve.
2. **Second graph:**
- Shows the curve with an upward-sloping tangent line crossing the curve at the learned point. This might represent a more accurate tangent determiner depending on the slope calculation.
3. **Third graph:**
- Features a downward-sloping tangent line interacting with the curve.
Each graph includes a small circle below it, likely intended for selection to identify which graph correctly visualizes the tangent line with respect to the curve's behavior at the point \( (2, 1) \).
**Instructions:**
Use a calculator or computer software to graph the function and correctly identify the tangent line through calculation.
This exercise intends to enhance understanding of differentiating curves and finding tangent lines by checking which graphical representation aligns with the theoretical calculation.
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