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Use the graph to find a. points where f ' ( x ) = 0 b. intervals where f ' ( x ) > 0 c. intervals where f ' ( x ) < 0

Use the graph to find a. points where f ' ( x ) = 0 b. intervals where f ' ( x ) > 0 c. intervals where f ' ( x ) < 0

Calculus: Early Transcendentals
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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Use the graph to find

a. points where f ' ( x ) = 0

b. intervals where f ' ( x ) > 0

c. intervals where f ' ( x ) < 0

The image depicts a graph of the function \( y = f(x) \) on a coordinate plane. Here's a detailed explanation: - **Axes:** The graph has two axes. The horizontal axis is labeled as \( x \) and the vertical axis is labeled as \( y \). - **Curve:** The function is represented by a smooth, pink curve that oscillates within the diagram. Various points along the curve are marked with small circles, indicating key points or possible critical points of the function. - **Grid:** The background consists of a grid of squares, suggesting that the graph is plotted on a standard Cartesian coordinate system. - **Scale and Intervals:** Both axes have visible grid lines and are marked at intervals of 1 unit, though no numerical labels are provided besides the origin marked as 0 on both axes. - **Behavior of the Function:** The function appears non-linear and exhibits several peaks and troughs, indicating changes in direction and concavity. It crosses the horizontal axis, which may suggest the locations of the roots or zeroes of the function. Overall, this graph is an illustrative depiction of a continuous, oscillating function, useful for visualizing concepts such as increasing/decreasing behavior, relative maxima and minima, and continuity.
Transcribed Image Text:The image depicts a graph of the function \( y = f(x) \) on a coordinate plane. Here's a detailed explanation: - **Axes:** The graph has two axes. The horizontal axis is labeled as \( x \) and the vertical axis is labeled as \( y \). - **Curve:** The function is represented by a smooth, pink curve that oscillates within the diagram. Various points along the curve are marked with small circles, indicating key points or possible critical points of the function. - **Grid:** The background consists of a grid of squares, suggesting that the graph is plotted on a standard Cartesian coordinate system. - **Scale and Intervals:** Both axes have visible grid lines and are marked at intervals of 1 unit, though no numerical labels are provided besides the origin marked as 0 on both axes. - **Behavior of the Function:** The function appears non-linear and exhibits several peaks and troughs, indicating changes in direction and concavity. It crosses the horizontal axis, which may suggest the locations of the roots or zeroes of the function. Overall, this graph is an illustrative depiction of a continuous, oscillating function, useful for visualizing concepts such as increasing/decreasing behavior, relative maxima and minima, and continuity.
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