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Find the graph given the following table. f'(x) 0 X a b с 0 1 Choose the correct graph below. O A. M.² 0 a b c O C. M. b c 0- 0 OB. 0 a b c O D. M 0 a b c ✔

Find the graph given the following table. f'(x) 0 X a b с 0 1 Choose the correct graph below. O A. M.² 0 a b c O C. M. b c 0- 0 OB. 0 a b c O D. M 0 a b c ✔

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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**Find the Graph Given the Following Table** | x | f'(x) | |---|-------| | a | 0 | | b | 0 | | c | 1 | **Choose the Correct Graph Below:** **Graph A:** - A curve that starts from a low point before \( a \), rises to a peak at \( a \), dips down, rises again to a peak at \( b \), and then continues upward at \( c \). The derivative at \( a \) and \( b \) are zero, indicating local maxima or minima, and the derivative at \( c \) is positive, indicating an upward slope. **Graph B:** - A graph that descends to a trough at \( a \), continues downward, and reaches a minimum at \( b \). Then it ascends; \( c \) shows a positive derivative, with the curve increasing at this point. **Graph C:** - A declining curve reaching minima at both \( a \) and \( b \), before ascending past \( c \) with a positive derivation. **Graph D:** - A layout where the curve rises to a peak at \( a \), falls to a distinct minimum at \( b \), then slopes upwards past \( c \) with a positive derivative. _To find the correct graph, analyze where the derivative \( f'(x) \) equals zero, signaling potential maxima or minima, and where it is positive, indicating an increasing function._
Transcribed Image Text:**Find the Graph Given the Following Table** | x | f'(x) | |---|-------| | a | 0 | | b | 0 | | c | 1 | **Choose the Correct Graph Below:** **Graph A:** - A curve that starts from a low point before \( a \), rises to a peak at \( a \), dips down, rises again to a peak at \( b \), and then continues upward at \( c \). The derivative at \( a \) and \( b \) are zero, indicating local maxima or minima, and the derivative at \( c \) is positive, indicating an upward slope. **Graph B:** - A graph that descends to a trough at \( a \), continues downward, and reaches a minimum at \( b \). Then it ascends; \( c \) shows a positive derivative, with the curve increasing at this point. **Graph C:** - A declining curve reaching minima at both \( a \) and \( b \), before ascending past \( c \) with a positive derivation. **Graph D:** - A layout where the curve rises to a peak at \( a \), falls to a distinct minimum at \( b \), then slopes upwards past \( c \) with a positive derivative. _To find the correct graph, analyze where the derivative \( f'(x) \) equals zero, signaling potential maxima or minima, and where it is positive, indicating an increasing function._
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