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Suppose that f(x) is continuous. The table below shows intervals where f'(x) and f"(x) are positive, negative, or zero. Draw a continuous graph that matches the information on the grid below. 0 < x < 1 1< x < 2 | 2< x < 33

Suppose that f(x) is continuous. The table below shows intervals where f'(x) and f"(x) are positive, negative, or zero. Draw a continuous graph that matches the information on the grid below. 0 < x < 1 1< x < 2 | 2< x < 33

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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### Understanding Continuity and Derivatives Suppose that \( f(x) \) is continuous. The following table displays the intervals where the first derivative \( f'(x) \) and the second derivative \( f''(x) \) are positive, negative, or zero. Your task is to draw a continuous graph that matches the information provided: | \( x \) | \( 0 < x < 1 \) | \( 1 < x < 2 \) | \( 2 < x < 3 \) | \( 3 < x < 4 \) | |---------------|-----------------|-----------------|-----------------|-----------------| | \( f'(x) \) | \( + \) | \( - \) | \( - \) | \( - \) | | \( f''(x) \) | \( - \) | \( - \) | \( + \) | \( 0 \) | **Analysis of the Derivative Table:** - **\( 0 < x < 1 \):** - \( f'(x) > 0 \): The function is increasing. - \( f''(x) < 0 \): The function is concave down. - **\( 1 < x < 2 \):** - \( f'(x) < 0 \): The function is decreasing. - \( f''(x) < 0 \): The function remains concave down. - **\( 2 < x < 3 \):** - \( f'(x) < 0 \): The function is still decreasing. - \( f''(x) > 0 \): The function changes to concave up. - **\( 3 < x < 4 \):** - \( f'(x) < 0 \): The function keeps decreasing. - \( f''(x) = 0 \): The concavity is neutral, suggesting an inflection point. **Graph Instructions:** Below the table, there is a blank grid with axes spanning from \(-1\) to 5 on both the x and y directions. Use the information from the table to sketch the corresponding graph: 1. **From \( x = 0 \) to \( x = 1 \):** - Draw an increasing curve with a concave
Transcribed Image Text:### Understanding Continuity and Derivatives Suppose that \( f(x) \) is continuous. The following table displays the intervals where the first derivative \( f'(x) \) and the second derivative \( f''(x) \) are positive, negative, or zero. Your task is to draw a continuous graph that matches the information provided: | \( x \) | \( 0 < x < 1 \) | \( 1 < x < 2 \) | \( 2 < x < 3 \) | \( 3 < x < 4 \) | |---------------|-----------------|-----------------|-----------------|-----------------| | \( f'(x) \) | \( + \) | \( - \) | \( - \) | \( - \) | | \( f''(x) \) | \( - \) | \( - \) | \( + \) | \( 0 \) | **Analysis of the Derivative Table:** - **\( 0 < x < 1 \):** - \( f'(x) > 0 \): The function is increasing. - \( f''(x) < 0 \): The function is concave down. - **\( 1 < x < 2 \):** - \( f'(x) < 0 \): The function is decreasing. - \( f''(x) < 0 \): The function remains concave down. - **\( 2 < x < 3 \):** - \( f'(x) < 0 \): The function is still decreasing. - \( f''(x) > 0 \): The function changes to concave up. - **\( 3 < x < 4 \):** - \( f'(x) < 0 \): The function keeps decreasing. - \( f''(x) = 0 \): The concavity is neutral, suggesting an inflection point. **Graph Instructions:** Below the table, there is a blank grid with axes spanning from \(-1\) to 5 on both the x and y directions. Use the information from the table to sketch the corresponding graph: 1. **From \( x = 0 \) to \( x = 1 \):** - Draw an increasing curve with a concave
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