Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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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Transcribed Image Text: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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