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Find the tangents to the graph shown below at the origin and the point (1, − 4). y 8x 11 10 $ $ # B- 2 -4- B The tangent to the curve at the origin is y= 0 The tangent to the curve at the point (1,-4) is y = (Simplify your answer.)

Find the tangents to the graph shown below at the origin and the point (1, − 4). y 8x 11 10 $ $ # B- 2 -4- B The tangent to the curve at the origin is y= 0 The tangent to the curve at the point (1,-4) is y = (Simplify your answer.)

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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**Graph Analysis and Problem-Solving Exercise** ### Task: Find the tangents to the graph shown below at the origin and the point (1, −4). #### Diagram: - The graph is plotted on a coordinate grid with the x-axis ranging from -10 to 10 and the y-axis from -10 to 10. - The graph features a blue curve representing the equation \( y = \frac{8x}{x^2 + 1} \). - The curve starts from the left side, increasing slightly, reaches a peak, then decreases sharply below the x-axis before rising again towards the right side. ### Questions: 1. The tangent to the curve at the origin is \( y = \_\_\_ \) 2. The tangent to the curve at the point (1, −4) is \( y = \_\_\_ \) (Simplify your answer.)
Transcribed Image Text:**Graph Analysis and Problem-Solving Exercise** ### Task: Find the tangents to the graph shown below at the origin and the point (1, −4). #### Diagram: - The graph is plotted on a coordinate grid with the x-axis ranging from -10 to 10 and the y-axis from -10 to 10. - The graph features a blue curve representing the equation \( y = \frac{8x}{x^2 + 1} \). - The curve starts from the left side, increasing slightly, reaches a peak, then decreases sharply below the x-axis before rising again towards the right side. ### Questions: 1. The tangent to the curve at the origin is \( y = \_\_\_ \) 2. The tangent to the curve at the point (1, −4) is \( y = \_\_\_ \) (Simplify your answer.)
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