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**Rich Activity #5** Sketch the graph of a function that satisfies all of the given conditions. - \( f'(0) = f'(4) = 0 \) - \( f'(x) = 1 \) if \( x < -1 \) - \( f'(x) > 0 \) if \( 0 < x < 2 \) - \( f'(x) < 0 \) if \( -1 < x < 0 \) or \( 2 < x < 4 \) or \( x > 4 \) - \( \lim_{x \to 2^-} f'(x) = -\infty \) - \( \lim_{x \to 2^+} f'(x) = +\infty \) - \( f''(x) > 0 \) if \( -1 < x < 2 \) or \( 2 < x < 4 \) - \( f''(x) < 0 \) if \( x > 4 \)

**Rich Activity #5** Sketch the graph of a function that satisfies all of the given conditions. - \( f'(0) = f'(4) = 0 \) - \( f'(x) = 1 \) if \( x < -1 \) - \( f'(x) > 0 \) if \( 0 < x < 2 \) - \( f'(x) < 0 \) if \( -1 < x < 0 \) or \( 2 < x < 4 \) or \( x > 4 \) - \( \lim_{x \to 2^-} f'(x) = -\infty \) - \( \lim_{x \to 2^+} f'(x) = +\infty \) - \( f''(x) > 0 \) if \( -1 < x < 2 \) or \( 2 < x < 4 \) - \( f''(x) < 0 \) if \( x > 4 \)

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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**Rich Activity #5** Sketch the graph of a function that satisfies all of the given conditions. - \( f'(0) = f'(4) = 0 \) - \( f'(x) = 1 \) if \( x < -1 \) - \( f'(x) > 0 \) if \( 0 < x < 2 \) - \( f'(x) < 0 \) if \( -1 < x < 0 \) or \( 2 < x < 4 \) or \( x > 4 \) - \( \lim_{x \to 2^-} f'(x) = -\infty \) - \( \lim_{x \to 2^+} f'(x) = +\infty \) - \( f''(x) > 0 \) if \( -1 < x < 2 \) or \( 2 < x < 4 \) - \( f''(x) < 0 \) if \( x > 4 \)
Transcribed Image Text:**Rich Activity #5** Sketch the graph of a function that satisfies all of the given conditions. - \( f'(0) = f'(4) = 0 \) - \( f'(x) = 1 \) if \( x < -1 \) - \( f'(x) > 0 \) if \( 0 < x < 2 \) - \( f'(x) < 0 \) if \( -1 < x < 0 \) or \( 2 < x < 4 \) or \( x > 4 \) - \( \lim_{x \to 2^-} f'(x) = -\infty \) - \( \lim_{x \to 2^+} f'(x) = +\infty \) - \( f''(x) > 0 \) if \( -1 < x < 2 \) or \( 2 < x < 4 \) - \( f''(x) < 0 \) if \( x > 4 \)
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