**Understanding the Parabola**Consider the parabola $ y = 4x - x^2 $.**(a) Find the slope of the tangent line to the parabola at the point $ (1, 3) $.**[Input box here for answer]**(b) Find an equation of the tangent line in part (a).**\[ y = \][Input box here for answer]**(c) Graph the parabola and the tangent line.****Explanation of Diagrams:**- The first graph (top-left) plots the red parabola $ y = 4x - x^2 $ and a blue line, a potential tangent line, intersecting the parabola at the point $ (1, 3) $ and extending in both directions. The parabola opens downwards and is centered around $ x = 2 $.- The second graph (top-right) also plots the parabola in red and a blue horizontal line, suggesting a potential tangent line, which does not touch the parabola at any single point but intersects it at two points, crossing the y-axis at around $ y = 10 $.- The third graph (bottom-left) includes the red parabola and a blue horizontal line below the x-axis, which does not intersect the parabola at any point, clearly not representing a tangent line.- The fourth graph (bottom-right) displays the red parabola and a blue line that appears to intersect the parabola at two points symmetrically, forming what could be a tangent at a single point if considered carefully but is less clear cut compared to the first graph.**Choose the correct graph that represents the parabola and the tangent line from the options provided.**[Multiple choice selection buttons under each graph]

consider the parabola y = 4x - x2. (a) Find the slope of the tangent line to the parabola at the point (1, 3). (b) Find an equation of the tangent line in part (a). y = (c) Graph the parabola and the tangent line.

consider the parabola y = 4x - x2. (a) Find the slope of the tangent line to the parabola at the point (1, 3). (b) Find an equation of the tangent line in part (a). y = (c) Graph the parabola and the tangent line.

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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Question

**Understanding the Parabola**

Consider the parabola $ y = 4x - x^2 $.

**(a) Find the slope of the tangent line to the parabola at the point $ (1, 3) $.**

[Input box here for answer]

**(b) Find an equation of the tangent line in part (a).**

\[ y = \]
[Input box here for answer]

**(c) Graph the parabola and the tangent line.**

**Explanation of Diagrams:**

- The first graph (top-left) plots the red parabola $ y = 4x - x^2 $ and a blue line, a potential tangent line, intersecting the parabola at the point $ (1, 3) $ and extending in both directions. The parabola opens downwards and is centered around $ x = 2 $.

- The second graph (top-right) also plots the parabola in red and a blue horizontal line, suggesting a potential tangent line, which does not touch the parabola at any single point but intersects it at two points, crossing the y-axis at around $ y = 10 $.

- The third graph (bottom-left) includes the red parabola and a blue horizontal line below the x-axis, which does not intersect the parabola at any point, clearly not representing a tangent line.

- The fourth graph (bottom-right) displays the red parabola and a blue line that appears to intersect the parabola at two points symmetrically, forming what could be a tangent at a single point if considered carefully but is less clear cut compared to the first graph.

**Choose the correct graph that represents the parabola and the tangent line from the options provided.**

[Multiple choice selection buttons under each graph]

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