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2 marksMathematicsConcavity, convexity and quasi-concavityTesting concavity and convexityModerateabout 2 min
DSE 2013 Question 22: Concavity, convexity and quasi-concavity
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The function f(x)=1/4x⁴-1/2x³-3x²+6 is: (A) concave on (-∞,2) and convex on (2,∞). (B) concave on (-1,2), convex on (-∞,-1) and (2,∞). (C) convex on (-1,2), concave on (-∞,-1) and (2,∞). (D) convex on (-∞,2) and concave on (2,∞).
Also written as: The function f(x)=1/4x^4-1/2x^3-3x^2+6 is:
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 DSE 2013 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.