W 1 2 y concave upward 3 concave downward Determine the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.) (0,1) U (3,00) (1,3) X 4 Nice work! X
W 1 2 y concave upward 3 concave downward Determine the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.) (0,1) U (3,00) (1,3) X 4 Nice work! X
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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Transcribed Image Text:You are given the graph of a function \( f \).
**Graph Description:**
- The graph shows a curve that begins at a high point on the y-axis, decreases to a minimum around \( x=1 \), rises to a peak around \( x=2 \), decreases again to a minimum around \( x=3 \), and then increases sharply.
- The x-axis is labeled from 0 to 4, and the y-axis is labeled with increments of 1.
**Task:**
Determine the intervals where the graph of \( f \) is concave upward and where it is concave downward. (Enter your answers using interval notation.)
- **Concave Upward:**
- Incorrectly entered as \( (0,1) \cup (3, \infty) \) with an "X" mark indicating it is incorrect.
- **Concave Downward:**
- Correctly entered as \( (1,3) \) with a "Nice work!" confirmation and a checkmark.
![**Problem Description:**
A stone is thrown straight up from the roof of a 256-ft building. The distance (in feet) of the stone from the ground at any time \( t \) (in seconds) is given by the equation:
\[ h(t) = -16t^2 + 96t + 256 \]
**Hint:** The stone is on the ground when \( h(t) = 0 \).
**Questions:**
1. **When is the stone rising?**
- Options:
- \( 0 \leq t < 8 \) (Correct)
- \( t < 3 \)
- \( t < 8 \)
- \( 8 < t < 3 \)
- \( t > 3 \)
- *Feedback:* Excellent job!
2. **When is the stone falling?**
- Options:
- \( t > 8 \) (Correct)
- \( 0 < t < 8 \)
- \( t > 3 \)
- \( 3 > t > 8 \)
- \( t < 3 \)
- *Feedback:* Nice work!
3. **If the stone were to miss the building, when would it hit the ground?**
- Answer: \( t = 3 \) sec
**Graph of \( h(t) \):**
The graph provided should depict a parabolic trajectory of the stone, with time (\( t \)) on the x-axis and height (\( h \)) on the y-axis. The graph is expected to show an initial rise to a peak (vertex of the parabola) followed by a descent back to the ground level. The peak of the parabola represents the highest point reached by the stone.
**Graph Layers Note:**
- A note is included explaining that after an object is added to the graph, "Graph Layers" can be used to view and edit its properties.
The graph tool shows a coordinate grid, indicating that further steps or interactions might be required to visualize the mathematical trajectory fully.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65b4ef97-4b38-4cee-a8cf-3ef6da10a16d%2F29abc327-c169-4772-856f-0f1e50a0f00d%2Fqg07jdt_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A stone is thrown straight up from the roof of a 256-ft building. The distance (in feet) of the stone from the ground at any time \( t \) (in seconds) is given by the equation:
\[ h(t) = -16t^2 + 96t + 256 \]
**Hint:** The stone is on the ground when \( h(t) = 0 \).
**Questions:**
1. **When is the stone rising?**
- Options:
- \( 0 \leq t < 8 \) (Correct)
- \( t < 3 \)
- \( t < 8 \)
- \( 8 < t < 3 \)
- \( t > 3 \)
- *Feedback:* Excellent job!
2. **When is the stone falling?**
- Options:
- \( t > 8 \) (Correct)
- \( 0 < t < 8 \)
- \( t > 3 \)
- \( 3 > t > 8 \)
- \( t < 3 \)
- *Feedback:* Nice work!
3. **If the stone were to miss the building, when would it hit the ground?**
- Answer: \( t = 3 \) sec
**Graph of \( h(t) \):**
The graph provided should depict a parabolic trajectory of the stone, with time (\( t \)) on the x-axis and height (\( h \)) on the y-axis. The graph is expected to show an initial rise to a peak (vertex of the parabola) followed by a descent back to the ground level. The peak of the parabola represents the highest point reached by the stone.
**Graph Layers Note:**
- A note is included explaining that after an object is added to the graph, "Graph Layers" can be used to view and edit its properties.
The graph tool shows a coordinate grid, indicating that further steps or interactions might be required to visualize the mathematical trajectory fully.
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