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:- **○ \( f' = 0 \)**---

Name: The given image shows a graph of a function. The graph includes a mar
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
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:**-