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1 . Find the point on the graph of 1+ x where the tangent line has the greatest slope.

1 . Find the point on the graph of 1+ x where the tangent line has the greatest slope.

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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The text on the image reads: "6. Find the point on the graph of \( y = \frac{x}{1 + x^2} \) where the tangent line has the greatest slope."
Transcribed Image Text:The text on the image reads: "6. Find the point on the graph of \( y = \frac{x}{1 + x^2} \) where the tangent line has the greatest slope."
The image displays a graph on a Cartesian plane. **Graph Description:** - The graph appears to be a single curve positioned in the right half of the plane. - The y-axis is labeled with integers, marked going both positively and negatively. - The x-axis is indicated but not explicitly labeled with values. - The graph appears to represent a hyperbolic or exponential decay curve, beginning high on the positive y-axis and approaching zero on the positive x-axis. - The curve has asymptotic behavior as it approaches both the x-axis and y-axis. This type of graph is often used to depict functions that model exponential decay, such as radioactive decay or cooling processes in physics. The asymptotic nature of the curve suggests that as the x-values increase, the function approaches but never actually reaches zero.
Transcribed Image Text:The image displays a graph on a Cartesian plane. **Graph Description:** - The graph appears to be a single curve positioned in the right half of the plane. - The y-axis is labeled with integers, marked going both positively and negatively. - The x-axis is indicated but not explicitly labeled with values. - The graph appears to represent a hyperbolic or exponential decay curve, beginning high on the positive y-axis and approaching zero on the positive x-axis. - The curve has asymptotic behavior as it approaches both the x-axis and y-axis. This type of graph is often used to depict functions that model exponential decay, such as radioactive decay or cooling processes in physics. The asymptotic nature of the curve suggests that as the x-values increase, the function approaches but never actually reaches zero.
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