**Question 29:** Identify the open interval(s) where \( f \) is concave up.- [A] \((-∞, -1)\)- [B] \((-∞, -3) \cup (-1, 2)\)- [C] \((-1, ∞)\)- [D] \((-2, 1)\) The image depicts the graph of the derivative of a function, denoted as \( f'(x) \).### Features of the Graph:- **Axes**: - The horizontal axis represents \( x \). - The vertical axis represents \( f'(x) \).- **Critical Points**: - The graph crosses the x-axis at approximately \( x = -2.5 \), \( x = 0 \), and \( x = 2 \). These are points where the derivative is zero, indicating potential local maxima or minima in the original function \( f(x) \).- **Behavior of the Graph**: - Starting from the left, the graph has a decreasing trend until just before \( x = -2.5 \). - After crossing the x-axis at \( x = -2.5 \), the graph increases and then decreases, crossing the x-axis again at \( x = 0 \). - The graph increases after \( x = 0 \) until just after \( x = 1.5 \), reaching a local maximum. - Beyond \( x = 2 \), the graph decreases sharply until it extends downward.- **Arrow Indicators**: - The arrows at the ends of the graph indicate that the behavior continues in those respective directions beyond the visible portion.### Interpretation:- **Increasing Intervals**: The function \( f(x) \) is increasing where \( f'(x) > 0 \). Based on the graph, this occurs approximately between \( -2.5 < x < 0 \) and \( 1.5 < x < 2.5 \).- **Decreasing Intervals**: The function \( f(x) \) is decreasing where \( f'(x) < 0 \). This is observed for \( x < -2.5 \), between \( 0 < x < 1.5 \), and \( x > 2.5 \).### Educational Context:Understanding the graph of the derivative is essential for identifying the behavior of the original function \( f(x) \). This includes recognizing intervals of increase or decrease, and identifying critical points that may correspond to local maxima, minima, or points of inflection in \( f(x) \). This knowledge is fundamental in calculus and helps in sketching and understanding the overall behavior of functions.

Answered: Identify the open interval(s) where f…

Identify the open interval(s) where f is concave up. [A] (-∞, -1) [B] (-∞, -3) U (-1,2) [C] (-1,00) [D] (-2,1)

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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