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7. Consider the graph of f', the derivative of f, that is given below. Use it to answer the following questions. a.) Where does f(x) have a local maximum? Explain how you know. b.) Where does f(x) have a local minimum? Explain how you know. -5- c.) Where is f concave up? Explain how you know. Answer in interval notation. جاتا 5 + -2-1 2+ 2 2 f'(x) 5 6 X

7. Consider the graph of f', the derivative of f, that is given below. Use it to answer the following questions. a.) Where does f(x) have a local maximum? Explain how you know. b.) Where does f(x) have a local minimum? Explain how you know. -5- c.) Where is f concave up? Explain how you know. Answer in interval notation. جاتا 5 + -2-1 2+ 2 2 f'(x) 5 6 X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. Consider the graph of f', the derivative of f, that is given below. Use it to answer the following questions. a.) Where does f(x) have a local maximum? Explain how you know. -5 -4 b.) Where does f(x) have a local minimum? Explain how you know. -5- c.) Where is f concave up? Explain how you know. Answer in interval notation. d.) Which is larger, f(-2) or f(-1), or is there not enough information to tell? Please explain. 8. Use Newton's method with the specified initial approximation x₁ to find x4, the fourth approximation to the root of the equation x3 - 4x² + 5 = 0, x₁ = 4. Show each approximation along the way. چتا y 3- 2- 2 f'(x) 4 6
Transcribed Image Text:7. Consider the graph of f', the derivative of f, that is given below. Use it to answer the following questions. a.) Where does f(x) have a local maximum? Explain how you know. -5 -4 b.) Where does f(x) have a local minimum? Explain how you know. -5- c.) Where is f concave up? Explain how you know. Answer in interval notation. d.) Which is larger, f(-2) or f(-1), or is there not enough information to tell? Please explain. 8. Use Newton's method with the specified initial approximation x₁ to find x4, the fourth approximation to the root of the equation x3 - 4x² + 5 = 0, x₁ = 4. Show each approximation along the way. چتا y 3- 2- 2 f'(x) 4 6
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