The given image shows a graph of a function. The graph includes a marked point which is indicated by a black dot. Here is the transcription and detailed explanation:---### Understanding the Derivative at a Point on a Function**Graph Description:**- The graph portrays a function `f(x)` with a marked black dot at a specific point on the curve.- The x-axis ranges from -5 to 5.- The y-axis ranges from -1 to 1, with horizontal grid lines at `y = -1`, `y = 0`, and `y = 1`.- The marked point appears to be at the peak of a local maximum near the x-coordinate of -2.**Question:**At the point shown on the function above, which of the following is true? - ○ $ f' = 0 $ - ○ $ f' < 0 $ - ○ $ f' > 0 $ **Explanation:**- The function appears to reach a local maximum at the marked point.- At a local maximum, the slope of the tangent to the curve is horizontal.- Therefore, the derivative of the function at this point is zero.By observing the graph, we can deduce that:#### At the point shown on the function above, the correct answer is:- **○ $ f' = 0 $**---

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Description: The given image shows a graph of a function. The graph includes a marked point which is indicated by a black dot. Here is the transcription and detailed explanation:---### Understanding the Derivative at a Point on a Function**Graph Description:**-

Answered: Image /qna-images/answer/4e5da42b-877f-4b10-a7aa-7752c01fd020.jpg

Answered: -5 -4 -3 -2 -1 1 2 3 4 5 At the point…

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-5 -4 -3 -2 -1 1 2 3 4 5 At the point shown on the function above, which of the following is true? Of' = 0 O f' < 0 O f'> 0

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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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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The given image shows a graph of a function. The graph includes a marked point which is indicated by a black dot. Here is the transcription and detailed explanation:

---

### Understanding the Derivative at a Point on a Function

**Graph Description:**
- The graph portrays a function `f(x)` with a marked black dot at a specific point on the curve.
- The x-axis ranges from -5 to 5.
- The y-axis ranges from -1 to 1, with horizontal grid lines at `y = -1`, `y = 0`, and `y = 1`.
- The marked point appears to be at the peak of a local maximum near the x-coordinate of -2.

**Question:**
At the point shown on the function above, which of the following is true?
- ○ $ f' = 0 $
- ○ $ f' < 0 $
- ○ $ f' > 0 $

**Explanation:**
- The function appears to reach a local maximum at the marked point.
- At a local maximum, the slope of the tangent to the curve is horizontal.
- Therefore, the derivative of the function at this point is zero.

By observing the graph, we can deduce that:

#### At the point shown on the function above, the correct answer is:
- **○ $ f' = 0 $**

---

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