**Problem Statement:**iv) Find the interval(s) where $ f(x) $ is concave down.v) Find the $ x $-values where any inflection points of $ f(x) $ occur.**Explanation:**- **Concavity and Intervals:** In calculus, a function is said to be concave down on an interval if its second derivative is negative over that interval. This indicates that the graph of the function is bending downwards.- **Inflection Points:** An inflection point occurs where the concavity of a function changes. This means the second derivative will change signs at these points.To solve these problems, you should:1. Calculate the second derivative of $ f(x) $.2. Determine where the second derivative is negative to find concave down intervals.3. Identify the $ x $-values where the second derivative changes from positive to negative or vice versa to find inflection points. **Text:**Use the graph of $ f'(x) $ shown below to answer each of the following. Note that the domain of $ f(x) $ is $(-\infty, c) \cup (c, \infty)$.**Graph Explanation:**The graph depicted is of the derivative $ f'(x) $. It features several key elements:- The horizontal axis is labeled $ x $, and the vertical axis is labeled $ f'(x) $.- The graph passes through the point labeled $ a $ and reaches a minimum at the origin $ 0 $.- The curve rises, passing through a vertical asymptote at $ x = c $, creating a discontinuity.- There are open circles at points $ b $ and $ e $, indicating undefined values of the derivative at these points.- The curve approaches a vertical asymptote between points $ d $ and continues into positive values as $ x $ increases.- The function $ f'(x) $ is negative between points $ a $ and $ d $, and positive after point $ d $.

Answered: Image /qna-images/answer/92aa168c-a7b5-4d6f-807f-a20b283c1541.jpg

Answered: Use the graph of f '(x) shown below to…

Use the graph of f '(x) shown below to answer each of the following. Note that the domain of f(z) is (-0, c) U (c, 0). at

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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Question

**Problem Statement:**

iv) Find the interval(s) where $ f(x) $ is concave down.

v) Find the $ x $-values where any inflection points of $ f(x) $ occur.

**Explanation:**

- **Concavity and Intervals:** In calculus, a function is said to be concave down on an interval if its second derivative is negative over that interval. This indicates that the graph of the function is bending downwards.

- **Inflection Points:** An inflection point occurs where the concavity of a function changes. This means the second derivative will change signs at these points.

To solve these problems, you should:

1. Calculate the second derivative of $ f(x) $.
2. Determine where the second derivative is negative to find concave down intervals.
3. Identify the $ x $-values where the second derivative changes from positive to negative or vice versa to find inflection points.

**Text:**

Use the graph of $ f'(x) $ shown below to answer each of the following. Note that the domain of $ f(x) $ is $(-\infty, c) \cup (c, \infty)$.

**Graph Explanation:**

The graph depicted is of the derivative $ f'(x) $. It features several key elements:

- The horizontal axis is labeled $ x $, and the vertical axis is labeled $ f'(x) $.
- The graph passes through the point labeled $ a $ and reaches a minimum at the origin $ 0 $.
- The curve rises, passing through a vertical asymptote at $ x = c $, creating a discontinuity.
- There are open circles at points $ b $ and $ e $, indicating undefined values of the derivative at these points.
- The curve approaches a vertical asymptote between points $ d $ and continues into positive values as $ x $ increases.
- The function $ f'(x) $ is negative between points $ a $ and $ d $, and positive after point $ d $.

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