Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x) = 7+x-x²: [0,3] ACCEN The absolute maximum value is atx=0 (Round to two decimal places as needed. Use a comma to separate answers as needed.) The absolute minimum value is a | at x = ₁ (Round to two decimal places as needed. Use a comma to separate answers as needed.) Af(x)
Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x) = 7+x-x²: [0,3] ACCEN The absolute maximum value is atx=0 (Round to two decimal places as needed. Use a comma to separate answers as needed.) The absolute minimum value is a | at x = ₁ (Round to two decimal places as needed. Use a comma to separate answers as needed.) Af(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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![### Problem
Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur.
\[ f(x) = 7 + x - \frac{x^2}{2} \]
Interval: \([0,3]\)
### Instructions for Input
- The absolute maximum value is \_\_\_ at \( x = \_\_\_\).
- The absolute minimum value is \_\_\_ at \( x = \_\_\_\).
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
### Graph Explanation
The graph displayed is a plot of the function \( f(x) = 7 + x - \frac{x^2}{2} \).
- The x-axis is labeled from -10 to 10.
- The y-axis is labeled from -10 to 10.
- The plotted curve shows a parabolic shape which opens downwards, indicating that the function has a maximum point within the interval.
By analyzing the graph in the specified domain \([0,3]\):
- There is an upward slope reaching a peak before it declines.
- The maximum and minimum values, as well as their corresponding x-values, should be identified by evaluating the function within this interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faed2933e-b67f-42a0-9fac-b6dce0e828b0%2Ffff20548-8ff3-4454-98f8-4c571b6fb85d%2Fsownai_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem
Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur.
\[ f(x) = 7 + x - \frac{x^2}{2} \]
Interval: \([0,3]\)
### Instructions for Input
- The absolute maximum value is \_\_\_ at \( x = \_\_\_\).
- The absolute minimum value is \_\_\_ at \( x = \_\_\_\).
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
### Graph Explanation
The graph displayed is a plot of the function \( f(x) = 7 + x - \frac{x^2}{2} \).
- The x-axis is labeled from -10 to 10.
- The y-axis is labeled from -10 to 10.
- The plotted curve shows a parabolic shape which opens downwards, indicating that the function has a maximum point within the interval.
By analyzing the graph in the specified domain \([0,3]\):
- There is an upward slope reaching a peak before it declines.
- The maximum and minimum values, as well as their corresponding x-values, should be identified by evaluating the function within this interval.
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