the second picture is part of the first picture, i could not fit it all in one screenshot. ### Graph of the Derivative of a Function#### Description:The figure represents the graph of the derivative, \( f' \), of a function \( f \) on the interval \([-3, 3]\).#### Graph Explanation:The graph features a sinusoidal curve that crosses the x-axis at three points: approximately \( x = -2 \), \( x = 0 \), and \( x = 2 \). The curve reaches its maximum point at \( x = -1 \) and its minimum point at \( x = 1 \).#### Determining Intervals of Increase and Decrease:To determine where \( f \) is increasing or decreasing, we observe where \( f' \), the derivative, is positive or negative, respectively. - \( f \) is increasing when \( f' \) is above the x-axis (positive).- \( f \) is decreasing when \( f' \) is below the x-axis (negative).#### Tasks:1. Determine the intervals on which \( f \) is increasing.2. Determine the intervals on which \( f \) is decreasing.(Use the symbol \( \cup \) for combining intervals, and the appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed.)---**Find the intervals where \( f \) is increasing:**\[ f \text{ is increasing on} \quad \_\_\_\_\_\_\_\_\_\_\_\_\_\ \]**Find the intervals where \( f \) is decreasing:**\[ f \text{ is decreasing on} \quad \_\_\_\_\_\_\_\_\_\_\_\_\_\ \]---### Solution Explanation:Use the graph to identify the intervals where the derivative is positive (above the x-axis) and negative (below the x-axis). From the graph:- \( f \) is increasing on intervals where \( f' \) > 0: - \( (-2, 0) \cup (2, 3) \) - \( f \) is decreasing on intervals where \( f' \) < 0: - \( (-3, -2) \cup (0, 2) \)Therefore,\[ f \text{ is increasing on} \quad (-2, 0) \cup (2, 3) \]\[ f \text{ is decreasing on} \ ---### Determining Concavity Intervals#### Determine the intervals on which \( f \) is concave down.(Use the symbol ∪ for combining intervals, and an appropriate type of parenthesis “\( ( \)”, “\[ \]” depending on whether the interval is open or closed.)\[ f \text{ is concave down on } \underline{\hspace{400px}} \]---#### Determine the intervals on which \( f \) is concave up.(Use the symbol ∪ for combining intervals, and an appropriate type of parenthesis “\( ( \)”, “\[ \]” depending on whether the interval is open or closed.)\[ f \text{ is concave up on } \underline{\hspace{400px}} \]---### Explanation:Concavity refers to the direction of the curvature of a graph:- **Concave Down**: The graph of \( f \) is concave down where it curves downwards like an upside-down cup. This occurs where the second derivative \( f''(x) \) is less than zero (\( f''(x) < 0 \)).- **Concave Up**: The graph of \( f \) is concave up where it curves upwards like a right-side-up cup. This occurs where the second derivative \( f''(x) \) is greater than zero (\( f''(x) > 0 \)).When determining concavity intervals, use:- **Parentheses \( (\ ) \)**: To denote open intervals (where the endpoint is not included).- **Brackets \([ ]\)**: To denote closed intervals (where the endpoint is included).- **Union \( \cup \)**: To combine multiple intervals.---This page is designed to help students understand and practice how to find and express the intervals where a function \( f \) is concave up or concave down.For additional assistance, review resources on calculus and concavity concepts.---

Answered: Image /qna-images/answer/c4941b04-05bc-4f5a-b0b4-d28ce1a9e7b0.jpg

Answered: The figure is the graph of the…

The figure is the graph of the derivative, f', of a function f on [-3,3]. 2+ 2 -2+ Determine the intervals on which ƒ is increasing.

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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