For the function g whose graph is given below, arrange the following numbers in increasing order. g'(-2) g'(0) g'(2) g'(4) y y = g(x) 3 4 < ? < ? ? く Explain your reasoning.

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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For the function \( g \) whose graph is given below, arrange the following numbers in increasing order.

- \( 0 \)
- \( g'(-2) \)
- \( g'(0) \)
- \( g'(2) \)
- \( g'(4) \)

![Graph Description]

The graph shows the curve of \( y = g(x) \). It is a smooth curve with the following key features:

- The curve dips down near \( x = -1 \), rises through \( x = 0 \), dips again between \( x = 1 \) and \( x = 2 \), and rises again after \( x = 2 \).
- The x-axis is labeled from \(-2\) to \(4\).
- The y-axis is labeled with the function \( y = g(x) \).

Below the graph, there is a sequence of dropdown menus each labeled with a "<" symbol. These are used to input the correct order of the numbers mentioned above.

**Task:**
Arrange the numbers \( 0 \), \( g'(-2) \), \( g'(0) \), \( g'(2) \), and \( g'(4) \) in increasing order using the graphical representation of the function \( g \).

**Explain your reasoning.** 

(Note: The derivatives \( g'(-2) \), \( g'(0) \), \( g'(2) \), and \( g'(4) \) represent the slopes of the tangent lines at those points on the graph.)
Transcribed Image Text:For the function \( g \) whose graph is given below, arrange the following numbers in increasing order. - \( 0 \) - \( g'(-2) \) - \( g'(0) \) - \( g'(2) \) - \( g'(4) \) ![Graph Description] The graph shows the curve of \( y = g(x) \). It is a smooth curve with the following key features: - The curve dips down near \( x = -1 \), rises through \( x = 0 \), dips again between \( x = 1 \) and \( x = 2 \), and rises again after \( x = 2 \). - The x-axis is labeled from \(-2\) to \(4\). - The y-axis is labeled with the function \( y = g(x) \). Below the graph, there is a sequence of dropdown menus each labeled with a "<" symbol. These are used to input the correct order of the numbers mentioned above. **Task:** Arrange the numbers \( 0 \), \( g'(-2) \), \( g'(0) \), \( g'(2) \), and \( g'(4) \) in increasing order using the graphical representation of the function \( g \). **Explain your reasoning.** (Note: The derivatives \( g'(-2) \), \( g'(0) \), \( g'(2) \), and \( g'(4) \) represent the slopes of the tangent lines at those points on the graph.)
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