Suppose you know that the function f is decreasing and concave down on t interval [2, 7]. which of the following statements is true about the values f'(x) and ƒ " (x) on the interval (2, 7)? O f'(x) > 0 and ƒ " (x) < 0 O f'(x) > 0 and f " (x) = 0 %3D O f'(x) > 0 and f" (x) > 0 O f'(x) = 0 and f" (x) < 0 O f'(x) = 0 and ƒ " (x) = 0 %3D O f'(x) = 0 and f" (x) > 0 O f'(æ) < 0 and f" (x) < 0 O f'(x) < 0 and ƒ " (x) = 0 O f'(x) < 0 and f" (x) > 0 None of the above are correct.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Suppose you know that the function f is decreasing and concave down on the
interval 2, 7|. Which of the following statements is true about the values of
f'(x) and f " (x) on the interval (2, 7)?
O f'(x) > 0 and f " (x) < 0
O f (x) > 0 and f" (x) = 0
O f'(x) > 0 and ƒ " (x) > 0
O f'(x) = 0 and f " (x) < 0
O f'(x) = 0 and f" (x) = 0
O f'(x) = 0 and f" (x) > 0
O f'(x) < 0 and f " (x) < 0
O f'(x) < 0 and f" (x) = 0
O f'(x) < 0 and f " (x) > 0
None of the above are correct.
Transcribed Image Text:Suppose you know that the function f is decreasing and concave down on the interval 2, 7|. Which of the following statements is true about the values of f'(x) and f " (x) on the interval (2, 7)? O f'(x) > 0 and f " (x) < 0 O f (x) > 0 and f" (x) = 0 O f'(x) > 0 and ƒ " (x) > 0 O f'(x) = 0 and f " (x) < 0 O f'(x) = 0 and f" (x) = 0 O f'(x) = 0 and f" (x) > 0 O f'(x) < 0 and f " (x) < 0 O f'(x) < 0 and f" (x) = 0 O f'(x) < 0 and f " (x) > 0 None of the above are correct.
Expert Solution
Step 1

If the first derivative of a function is negative then the function is decreasing and vice versa.

similarly if the second derivative is negative then the function is concave down and vice versa.

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