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7. Sketch f on the grid below given the following conditions. f'>0 f">0 f'<0 f">0 f'>0 f"<0 f'<0 f"<0 -2 -1 where f(-2)=-16, f(-1)=-5 & f(0) = 0 -8 -10- -14- -16-

7. Sketch f on the grid below given the following conditions. f'>0 f">0 f'<0 f">0 f'>0 f"<0 f'<0 f"<0 -2 -1 where f(-2)=-16, f(-1)=-5 & f(0) = 0 -8 -10- -14- -16-

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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**Educational Website Content:** **Exercise 7: Graphical Sketching of Functions** **Task:** Sketch the function \( f \) on the provided grid using the given conditions. **Conditions:** - **Interval:** From \(-2\) to \(0\) - \( f' < 0 \), \( f'' > 0 \) - **Interval:** From \(-1\) to \(0\) - \( f' > 0 \), \( f'' < 0 \) - **Key Function Points:** - \( f(-2) = -16 \) - \( f(-1) = -5 \) - \( f(0) = 0 \) **Graph Explanation:** The grid has axes labeled \( x \) and \( y \), with scales clearly marked every 1 unit along both axes. The focus should be on sketching a curve that fulfills the conditions of increasing or decreasing behavior (\( f' \)) as well as concavity (\( f'' \)) on specified intervals. The curve features should reflect these derivative conditions: - From \( x = -2 \) to \( x = -1 \), the curve should be decreasing and concave up. - From \( x = -1 \) to \( x = 0 \), the curve should be increasing and concave down. By following these guidelines, you can accurately sketch a qualitative representation of the function on the grid.
Transcribed Image Text:**Educational Website Content:** **Exercise 7: Graphical Sketching of Functions** **Task:** Sketch the function \( f \) on the provided grid using the given conditions. **Conditions:** - **Interval:** From \(-2\) to \(0\) - \( f' < 0 \), \( f'' > 0 \) - **Interval:** From \(-1\) to \(0\) - \( f' > 0 \), \( f'' < 0 \) - **Key Function Points:** - \( f(-2) = -16 \) - \( f(-1) = -5 \) - \( f(0) = 0 \) **Graph Explanation:** The grid has axes labeled \( x \) and \( y \), with scales clearly marked every 1 unit along both axes. The focus should be on sketching a curve that fulfills the conditions of increasing or decreasing behavior (\( f' \)) as well as concavity (\( f'' \)) on specified intervals. The curve features should reflect these derivative conditions: - From \( x = -2 \) to \( x = -1 \), the curve should be decreasing and concave up. - From \( x = -1 \) to \( x = 0 \), the curve should be increasing and concave down. By following these guidelines, you can accurately sketch a qualitative representation of the function on the grid.
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