Match List I (sign of first and second derivatives) with List II (shape of the curve).
List I
A. f'(x) > 0 and f''(x) > 0
B. f'(x) > 0 and f''(x) < 0
C. f'(x) < 0 and f''(x) < 0
D. f'(x) < 0 and f''(x) > 0.
List II
I. increasing and concave (rises at a decreasing rate)
II. decreasing and concave (falls at an increasing rate)
III. decreasing and convex (falls at a decreasing rate)
IV. increasing and convex (rises at an increasing rate).
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Concavity, convexity and quasi-concavity has come up 39 times in 6 exams since 2006.
What this question tests
This question is on Testing concavity and convexity, part of Concavity, convexity and quasi-concavity in Mathematics.
Checking concavity or convexity from a definition, derivatives or operations that preserve it.
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Question from the UGC-NET 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.
