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7. Sketch the graph of a function f that satisfies the given conditions: f(0) = 3; f(-2) = f(2) = -4 f'(-2) = f'(2) = 0; f'(0) is undefined f'(x) > 0 i- 2 < x< 0 and x> 2 f'(x) < 0 if x < -2 or 0 < x < 2

7. Sketch the graph of a function f that satisfies the given conditions: f(0) = 3; f(-2) = f(2) = -4 f'(-2) = f'(2) = 0; f'(0) is undefined f'(x) > 0 i- 2 < x< 0 and x> 2 f'(x) < 0 if x < -2 or 0 < x < 2

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 Function Graph** **Objective:** Sketch the graph of a function \( f \) that satisfies the given conditions. **Conditions:** 1. \( f(0) = 3 \); \( f(-2) = f(2) = -4 \) 2. \( f'(-2) = f'(2) = 0 \); \( f'(0) \) is undefined 3. \( f'(x) > 0 \) if \(-2 < x < 0\) and \(x > 2\) 4. \( f'(x) < 0 \) if \(x < -2\) or \(0 < x < 2\) **Graph Explanation:** - **Axes:** The diagram includes a Cartesian plane with evenly spaced grid lines marking the x and y axes. - **Key Points:** Plot the points \((0, 3)\), \((-2, -4)\), and \((2, -4)\). - **Derivative Info:** - At \(x = -2\) and \(x = 2\), the slope is zero, indicating local maxima or minima. - At \(x = 0\), the slope is undefined, suggesting a possible cusp or vertical tangent. - **Intervals of Increase/Decrease:** - Increasing: \(-2 < x < 0\) and \(x > 2\) - Decreasing: \(x < -2\) and \(0 < x < 2\) **Instructions for Sketching:** - Begin the graph at the point \((-2, -4)\), increasing until it reaches \(x=0\). - Decrease towards the point \((2, -4)\). - Ensure a horizontal tangent at \(x = -2\) and \(x = 2\). - Mark any sharp turns or cusps at \(x = 0\) as the derivative is undefined.
Transcribed Image Text:**Instructions for Sketching a Function Graph** **Objective:** Sketch the graph of a function \( f \) that satisfies the given conditions. **Conditions:** 1. \( f(0) = 3 \); \( f(-2) = f(2) = -4 \) 2. \( f'(-2) = f'(2) = 0 \); \( f'(0) \) is undefined 3. \( f'(x) > 0 \) if \(-2 < x < 0\) and \(x > 2\) 4. \( f'(x) < 0 \) if \(x < -2\) or \(0 < x < 2\) **Graph Explanation:** - **Axes:** The diagram includes a Cartesian plane with evenly spaced grid lines marking the x and y axes. - **Key Points:** Plot the points \((0, 3)\), \((-2, -4)\), and \((2, -4)\). - **Derivative Info:** - At \(x = -2\) and \(x = 2\), the slope is zero, indicating local maxima or minima. - At \(x = 0\), the slope is undefined, suggesting a possible cusp or vertical tangent. - **Intervals of Increase/Decrease:** - Increasing: \(-2 < x < 0\) and \(x > 2\) - Decreasing: \(x < -2\) and \(0 < x < 2\) **Instructions for Sketching:** - Begin the graph at the point \((-2, -4)\), increasing until it reaches \(x=0\). - Decrease towards the point \((2, -4)\). - Ensure a horizontal tangent at \(x = -2\) and \(x = 2\). - Mark any sharp turns or cusps at \(x = 0\) as the derivative is undefined.
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