Please help me with this problem. Thank you! ### Tangent Line Problem**Objective:** Find an equation of the tangent line to the graph of the function at the given point.**Function and Point:** \[ y = \frac{1}{3}x^3 + 8x, \quad (2, 2) \]**Equation of the Tangent Line:** \[ y = \text{\_\_\_\_\_} \]**Instructions:** Use a graphing utility to graph the function and the tangent line in the same viewing window.### Graphs Explanation#### Graph 1:In the first graph:- **Axes:** The horizontal axis represents $x$, and the vertical axis represents $y$. Axis values range from -7 to 7.- **Curves:** - The **blue curve** is the graph of the function $y = \frac{1}{3}x^3 + 8x$. - The **red line** is the tangent line at the point (2, 2).- **Behavior:** - The blue curve enters the window from the left going down, curves near the origin, passes through the point (2, 2), and continues upward. - The red line, representing the tangent, touches the curve at (2, 2) and extends with a slight upward slope.#### Graph 2:In the second graph:- Similar axes and curve representations, but the graph is shifted showing more of the upper segment of the function and tangent, emphasizing their intersection point.#### Graph 3:In the third graph:- The axes remain the same.- **Additional Observations:** - The tangent line is seen more prominently, showing its linear trajectory through (2, 2) as it descends.**Information Note:**The small information icons on each graph probably provide further explanations or allow interactions to better understand the tangent line's behavior in relation to the curve.### ConclusionThe visual representations clearly demonstrate the interaction between the function and its tangent line at the specified point. Adjust graph views as needed for better analysis when using graphing utilities.

Name: Please help me with this problem. Thank you! ### Tangent Line Problem
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Description: Please help me with this problem. Thank you! ### Tangent Line Problem**Objective:** Find an equation of the tangent line to the graph of the function at the given point.**Function and Point:** \[ y = \frac{1}{3}x^3 + 8x, \quad (2, 2) \]**Equation

Answered: Image /qna-images/answer/0476611a-c695-4a0f-97ee-21a3d310711f.jpg

Math

Calculus

Find an equation of the tangent line to the graph of the function at the given point. y =V2x + 8x, (2, 2) y = Use a graphing utility to graph the function and the tangent line in the same viewing window. y 7 6 4 3 2 2 The xyteodrdirtete'nighe-gnten.There durrt ertdine o the Zrefi 5-4 -3-21 1 2 3 4 5 6 7 • The curve enters the windtow.in the second quadrant, goes down and right becomit more steep, passes through the origin nearly vertical, ggs down and rightbecoming less steep, passes through the point (2, -2) touching he line, and exits the window The fourth quadrant. • The line enters the winsw in the second quadrant, goes down and right, crosseg the x-axis at x -3, crosses the y-axis at y-1.2, pass through the point (2, -2) touching the curve, andexits the window in the fourth quadrant. -7-6-8-4-3-2-1, 1 2 3 4 5 6 7 -7-6-5-43-2-1, 1 2 3 4 5 6 7 -2 -3 -3 -4 -4 -5 -5 -6 -6 2 -7-6-5-4-3-2- 1 2 3 45 6 7

Find an equation of the tangent line to the graph of the function at the given point. y =V2x + 8x, (2, 2) y = Use a graphing utility to graph the function and the tangent line in the same viewing window. y 7 6 4 3 2 2 The xyteodrdirtete'nighe-gnten.There durrt ertdine o the Zrefi 5-4 -3-21 1 2 3 4 5 6 7 • The curve enters the windtow.in the second quadrant, goes down and right becomit more steep, passes through the origin nearly vertical, ggs down and rightbecoming less steep, passes through the point (2, -2) touching he line, and exits the window The fourth quadrant. • The line enters the winsw in the second quadrant, goes down and right, crosseg the x-axis at x -3, crosses the y-axis at y-1.2, pass through the point (2, -2) touching the curve, andexits the window in the fourth quadrant. -7-6-8-4-3-2-1, 1 2 3 4 5 6 7 -7-6-5-43-2-1, 1 2 3 4 5 6 7 -2 -3 -3 -4 -4 -5 -5 -6 -6 2 -7-6-5-4-3-2- 1 2 3 45 6 7

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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Please help me with this problem. Thank you!

### Tangent Line Problem

**Objective:**
Find an equation of the tangent line to the graph of the function at the given point.

**Function and Point:**
\[ y = \frac{1}{3}x^3 + 8x, \quad (2, 2) \]

**Equation of the Tangent Line:**
\[ y = \text{\_\_\_\_\_} \]

**Instructions:**
Use a graphing utility to graph the function and the tangent line in the same viewing window.

### Graphs Explanation

#### Graph 1:
In the first graph:
- **Axes:** The horizontal axis represents $x$, and the vertical axis represents $y$. Axis values range from -7 to 7.
- **Curves:**
- The **blue curve** is the graph of the function $y = \frac{1}{3}x^3 + 8x$.
- The **red line** is the tangent line at the point (2, 2).
- **Behavior:**
- The blue curve enters the window from the left going down, curves near the origin, passes through the point (2, 2), and continues upward.
- The red line, representing the tangent, touches the curve at (2, 2) and extends with a slight upward slope.

#### Graph 2:
In the second graph:
- Similar axes and curve representations, but the graph is shifted showing more of the upper segment of the function and tangent, emphasizing their intersection point.

#### Graph 3:
In the third graph:
- The axes remain the same.
- **Additional Observations:**
- The tangent line is seen more prominently, showing its linear trajectory through (2, 2) as it descends.

**Information Note:**
The small information icons on each graph probably provide further explanations or allow interactions to better understand the tangent line's behavior in relation to the curve.

### Conclusion

The visual representations clearly demonstrate the interaction between the function and its tangent line at the specified point. Adjust graph views as needed for better analysis when using graphing utilities.

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