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7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 N -3 -4 -5 -6 1 2 3 4 5 6 7

7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 N -3 -4 -5 -6 1 2 3 4 5 6 7

Calculus: Early Transcendentals
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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Over the interval \((- \infty, \infty)\), this function is: - ○ concave up \((f'' > 0)\) - ○ concave down \((f'' < 0)\)
Transcribed Image Text:Over the interval \((- \infty, \infty)\), this function is: - ○ concave up \((f'' > 0)\) - ○ concave down \((f'' < 0)\)
Below is the function \( f(x) \). The graph displays a parabola that opens upwards. The graph is plotted on a coordinate plane with the x-axis ranging from -7 to 7, and the y-axis from -7 to 7. The vertex of the parabola is at the point (-1, -3), indicating that this is the minimum point of the function. The curve is symmetric about the vertical line \( x = -1 \). **Graph Characteristics:** - The parabola decreases for \( x < -1 \) and increases for \( x > -1 \). **Questions:** 1. Over which interval of \( x \) values is \( f' > 0 \)? - \(( -1, \infty )\) - \([ -1, \infty )\) - \(( -\infty, -1 )\) - \(( -\infty, -1 ]\) - \(( -\infty, \infty )\) 2. Over which interval of \( x \) values is \( f' < 0 \)? - \(( -1, \infty )\) - \([ -1, \infty )\) - \(( -\infty, -1 )\) - \(( -\infty, -1 ]\) These questions are designed to assess understanding of the intervals where the function is increasing or decreasing, which corresponds to where the derivative is positive or negative respectively.
Transcribed Image Text:Below is the function \( f(x) \). The graph displays a parabola that opens upwards. The graph is plotted on a coordinate plane with the x-axis ranging from -7 to 7, and the y-axis from -7 to 7. The vertex of the parabola is at the point (-1, -3), indicating that this is the minimum point of the function. The curve is symmetric about the vertical line \( x = -1 \). **Graph Characteristics:** - The parabola decreases for \( x < -1 \) and increases for \( x > -1 \). **Questions:** 1. Over which interval of \( x \) values is \( f' > 0 \)? - \(( -1, \infty )\) - \([ -1, \infty )\) - \(( -\infty, -1 )\) - \(( -\infty, -1 ]\) - \(( -\infty, \infty )\) 2. Over which interval of \( x \) values is \( f' < 0 \)? - \(( -1, \infty )\) - \([ -1, \infty )\) - \(( -\infty, -1 )\) - \(( -\infty, -1 ]\) These questions are designed to assess understanding of the intervals where the function is increasing or decreasing, which corresponds to where the derivative is positive or negative respectively.
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