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f(x) = 2x? + 2x + 4 a) Find f'(x). 4x+2 b) Identify the graph that displays f in blue and f' in red. D 10 А. F10 1,0 10 -10 10 10 10 -10 10 B.

f(x) = 2x? + 2x + 4 a) Find f'(x). 4x+2 b) Identify the graph that displays f in blue and f' in red. D 10 А. F10 1,0 10 -10 10 10 10 -10 10 B.

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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## Problem Statement Given the function \( f(x) = 2x^2 + 2x + 4 \), complete the following tasks: ### a) Find \( f'(x) \). **Solution:** The derivative of the function is \( f'(x) = 4x + 2 \). ### b) Identify the graph that displays \( f \) in blue and \( f' \) in red. **Options:** - **Graph A:** - **Blue Curve:** Represents a parabola opening upwards. This is likely the graph of the original function \( f(x) = 2x^2 + 2x + 4 \). - **Red Line:** Represents a straight line with a positive slope, consistent with the derivative \( f'(x) = 4x + 2 \). - **Graph B:** - **Blue Curve:** Also depicts a parabola opening upwards. - **Red Line:** Displays a linear function, again indicating the graph of \( f'(x) \). In Graph A, the intersection points and the slopes differentiate \( f \) in blue and \( f' \) in red. However, Graph B presents similar features. ### Conclusion: Select the graph that correctly corresponds to \( f \) in blue and \( f' \) in red.
Transcribed Image Text:## Problem Statement Given the function \( f(x) = 2x^2 + 2x + 4 \), complete the following tasks: ### a) Find \( f'(x) \). **Solution:** The derivative of the function is \( f'(x) = 4x + 2 \). ### b) Identify the graph that displays \( f \) in blue and \( f' \) in red. **Options:** - **Graph A:** - **Blue Curve:** Represents a parabola opening upwards. This is likely the graph of the original function \( f(x) = 2x^2 + 2x + 4 \). - **Red Line:** Represents a straight line with a positive slope, consistent with the derivative \( f'(x) = 4x + 2 \). - **Graph B:** - **Blue Curve:** Also depicts a parabola opening upwards. - **Red Line:** Displays a linear function, again indicating the graph of \( f'(x) \). In Graph A, the intersection points and the slopes differentiate \( f \) in blue and \( f' \) in red. However, Graph B presents similar features. ### Conclusion: Select the graph that correctly corresponds to \( f \) in blue and \( f' \) in red.
The image contains a graph with two intersecting plots. The blue curve represents a quadratic function, forming a parabola that opens upwards. The red line represents a linear function. The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10 as well. Below the graph, the text reads: "c) Use interval notation to indicate where the graph is increasing and where it is decreasing." "NOTE: When entering your answers, remember that: You use 'INF' for ∞ and '-INF' for -∞. And use 'U' for the union symbol. Enter DNE if an answer does not exist." "f is increasing on [text box]" "f is decreasing on [text box]" This section is likely part of an educational module focusing on identifying intervals of increase and decrease for given functions using interval notation.
Transcribed Image Text:The image contains a graph with two intersecting plots. The blue curve represents a quadratic function, forming a parabola that opens upwards. The red line represents a linear function. The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10 as well. Below the graph, the text reads: "c) Use interval notation to indicate where the graph is increasing and where it is decreasing." "NOTE: When entering your answers, remember that: You use 'INF' for ∞ and '-INF' for -∞. And use 'U' for the union symbol. Enter DNE if an answer does not exist." "f is increasing on [text box]" "f is decreasing on [text box]" This section is likely part of an educational module focusing on identifying intervals of increase and decrease for given functions using interval notation.
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