If the function is concave, then
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4 marks, −1MathematicsConcavity, convexity and quasi-concavityConvex sets and functionsModerateabout 2 min
DSE 2018 Question 47: Concavity, convexity and quasi-concavity
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If the function f: ℝ² → ℝ is concave, then (A) {(x,r) ∈ ℝ² × ℝ | f(x) < r} is convex (B) {(x,r) ∈ ℝ² × ℝ | f(x) = r} is convex (C) {(x,r) ∈ ℝ² × ℝ | f(x) ≥ r} is convex (D) {(x,r) ∈ ℝ² × ℝ | f(x) ≤ r} is convex
Also written as: If the function f: R^2 -> R is concave, then
Concavity, convexity and quasi-concavity has come up 39 times in 6 exams since 2006.
What this question tests
This question is on Convex sets and functions, part of Concavity, convexity and quasi-concavity in Mathematics.
Sets and functions with no dents, and the inequalities that define them.
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Question from the DSE 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.