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Use the graph at right for questions 4 and 5. It consists of a semicircle and two line segments. 4. f(x) = 0 for x = A. 1 B. 2 C. 4 D. 1 and 4 5. f(x) does not exist for x = A. 1 only B. 1 and 2 C. 2 and 6 D. 0, 1, 2, and 6 2 f(x) X

Use the graph at right for questions 4 and 5. It consists of a semicircle and two line segments. 4. f(x) = 0 for x = A. 1 B. 2 C. 4 D. 1 and 4 5. f(x) does not exist for x = A. 1 only B. 1 and 2 C. 2 and 6 D. 0, 1, 2, and 6 2 f(x) 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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**Graph Description:** The graph depicted shows a function \( f(x) \) consisting of a semicircle and two line segments. The semicircle is situated in the positive quadrant of the coordinate system, spanning from \( x = 2 \) to \( x = 6 \) with a peak at \( y = 2 \). The left segment descends from point \( (0, 0) \) through \( (1, -2) \) to \( (2, 0) \), forming a V-shape at \( (1, -2) \). **Transcription:** Use the graph at right for questions 4 and 5. It consists of a semicircle and two line segments. 4. \( f'(x) = 0 \) for \( x = \) A. 1 B. 2 C. 4 D. 1 and 4 5. \( f'(x) \) does not exist for \( x = \) A. 1 only B. 1 and 2 C. 2 and 6 D. 0, 1, 2, and 6 6. Given that \( f(-3) = 4 \) and \( f'(-3) = 2 \), which of the following is the tangent line approximation of \( f(-3.1) \) ? A. 4.2 B. 4.1 C. 3.9 D. 3.8 7. If the line \( 3x - 5y = 7 \) is tangent to the graph of \( f \) at the point where \( x = 4 \) then \(\frac{f(4+h)-f(4)}{h}\) A. \( \frac{3}{5} \) B. \( \frac{5}{3} \) C. 3 D. 5
Transcribed Image Text:**Graph Description:** The graph depicted shows a function \( f(x) \) consisting of a semicircle and two line segments. The semicircle is situated in the positive quadrant of the coordinate system, spanning from \( x = 2 \) to \( x = 6 \) with a peak at \( y = 2 \). The left segment descends from point \( (0, 0) \) through \( (1, -2) \) to \( (2, 0) \), forming a V-shape at \( (1, -2) \). **Transcription:** Use the graph at right for questions 4 and 5. It consists of a semicircle and two line segments. 4. \( f'(x) = 0 \) for \( x = \) A. 1 B. 2 C. 4 D. 1 and 4 5. \( f'(x) \) does not exist for \( x = \) A. 1 only B. 1 and 2 C. 2 and 6 D. 0, 1, 2, and 6 6. Given that \( f(-3) = 4 \) and \( f'(-3) = 2 \), which of the following is the tangent line approximation of \( f(-3.1) \) ? A. 4.2 B. 4.1 C. 3.9 D. 3.8 7. If the line \( 3x - 5y = 7 \) is tangent to the graph of \( f \) at the point where \( x = 4 \) then \(\frac{f(4+h)-f(4)}{h}\) A. \( \frac{3}{5} \) B. \( \frac{5}{3} \) C. 3 D. 5
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