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Sketch (on your work paper) the graph of a single continuous function f(x) that meets all the following conditions. Do not input anything in the answer box below. ● ● f'(x) = 0 for x = f'(x) is undefined for x = 7 f'(x)> 0 for 4 < x < 3 and x > 7 f'(x) < 0 for x < -4 and 3 < x < 7 ƒ''(x) 0 for x 2 = f''(x) is undefined for x = 7 f''(x) > 0 for x < -2 f''(x) < 0 for 2 < x < 7 and x > 7 -4, x = 3

Sketch (on your work paper) the graph of a single continuous function f(x) that meets all the following conditions. Do not input anything in the answer box below. ● ● f'(x) = 0 for x = f'(x) is undefined for x = 7 f'(x)> 0 for 4 < x < 3 and x > 7 f'(x) < 0 for x < -4 and 3 < x < 7 ƒ''(x) 0 for x 2 = f''(x) is undefined for x = 7 f''(x) > 0 for x < -2 f''(x) < 0 for 2 < x < 7 and x > 7 -4, x = 3

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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**Instructions for Sketching a Continuous Function \( f(x) \)** You are tasked with sketching the graph of a single continuous function \( f(x) \) that satisfies the following conditions: 1. \( f'(x) = 0 \) at \( x = -4 \) and \( x = 3 \) 2. \( f'(x) \) is undefined for \( x = 7 \) 3. \( f'(x) > 0 \) for \( -4 < x < 3 \) and \( x > 7 \) 4. \( f'(x) < 0 \) for \( x < -4 \) and \( 3 < x < 7 \) 5. \( f''(x) = 0 \) at \( x = -2 \) 6. \( f''(x) \) is undefined for \( x = 7 \) 7. \( f''(x) > 0 \) for \( x < -2 \) 8. \( f''(x) < 0 \) for \( -2 < x < 7 \) and \( x > 7 \) **Diagram Description** - **Critical Points Analysis**: At \( x = -4 \) and \( x = 3 \), the function has critical points where the first derivative is zero, indicating possible extrema. - **Undefined Derivative at \( x = 7 \)**: The first derivative being undefined suggests a cusp or a vertical tangent at this point. - **Monotonicity**: - Interval \( -4 < x < 3 \) and \( x > 7 \): \( f(x) \) is increasing. - Interval \( x < -4 \) and \( 3 < x < 7 \): \( f(x) \) is decreasing. - **Concavity**: - At \( x = -2 \): Inflection point where second derivative changes sign. - Interval \( x < -2 \): Concave up. - Interval \( -2 < x < 7 \) and \( x > 7 \): Concave down. These conditions help in structuring the sketch of \( f(x) \) with the appropriate curvature and slope behavior at specified points and intervals.
Transcribed Image Text:**Instructions for Sketching a Continuous Function \( f(x) \)** You are tasked with sketching the graph of a single continuous function \( f(x) \) that satisfies the following conditions: 1. \( f'(x) = 0 \) at \( x = -4 \) and \( x = 3 \) 2. \( f'(x) \) is undefined for \( x = 7 \) 3. \( f'(x) > 0 \) for \( -4 < x < 3 \) and \( x > 7 \) 4. \( f'(x) < 0 \) for \( x < -4 \) and \( 3 < x < 7 \) 5. \( f''(x) = 0 \) at \( x = -2 \) 6. \( f''(x) \) is undefined for \( x = 7 \) 7. \( f''(x) > 0 \) for \( x < -2 \) 8. \( f''(x) < 0 \) for \( -2 < x < 7 \) and \( x > 7 \) **Diagram Description** - **Critical Points Analysis**: At \( x = -4 \) and \( x = 3 \), the function has critical points where the first derivative is zero, indicating possible extrema. - **Undefined Derivative at \( x = 7 \)**: The first derivative being undefined suggests a cusp or a vertical tangent at this point. - **Monotonicity**: - Interval \( -4 < x < 3 \) and \( x > 7 \): \( f(x) \) is increasing. - Interval \( x < -4 \) and \( 3 < x < 7 \): \( f(x) \) is decreasing. - **Concavity**: - At \( x = -2 \): Inflection point where second derivative changes sign. - Interval \( x < -2 \): Concave up. - Interval \( -2 < x < 7 \) and \( x > 7 \): Concave down. These conditions help in structuring the sketch of \( f(x) \) with the appropriate curvature and slope behavior at specified points and intervals.
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