Consider a function , where denotes the set of real numbers. If is increasing, i.e., implies , then
Tap an option to check your answer.
1 markMathematicsConcavity, convexity and quasi-concavityQuasi-concavity and quasi-convexityModerateabout 2 min
DSE 2006 Question 15: Concavity, convexity and quasi-concavity
Answer and worked solution
Checking your account…
Plain-text version
Consider a function f:ℜ→ℜ, where ℜ denotes the set of real numbers. If f is increasing, i.e., x≥ y implies f(x)≥ f(y), then (A) f is concave (B) f is convex (C) f is quasi-convex (D) f is continuous
Also written as: Consider a function f: Re -> Re, where Re denotes the set of real numbers. If f is increasing, i.e., x>= y implies f(x)>= f(y), then
Concavity, convexity and quasi-concavity has come up 39 times in 6 exams since 2006.
What this question tests
This question is on Quasi-concavity and quasi-convexity, part of Concavity, convexity and quasi-concavity in Mathematics.
The weaker shape conditions defined by upper or lower level sets.
TestStop has 8 past-paper questions on this subtopic; the nearest in year are below.
Similar questions from other papers
- Which of the following statements is not correct?
- Let S₁ = {(x,y) ∈ R²: x + y ≥ 1, x + y ≤ 2, y ≥ x², x,y ≥ 0} and S₂ = {(x,y) ∈ R²: x + y ≥ 1, x + y ≤ 2, y ≤ x², x,y ≥ 0}. Then, which of the following is CORRECT?
- A function is strictly concave in the interval I, if for all a, b ∈ I and λ ∈ (0, 1) 1. f[(1-λ)a + λ b] > (1-λ)f(a) + λ f(b) 2. f[(1-λ)a + λ b] < (1-λ)f(a) + λ f(b) 3.
- The function e^(-1/2x²) is:
- Let f, g: ℝ → ℝ be f(x)=x+2 for x≤1, 2x+1 for x>1; and g(x)=2x for x≤2, x+2 for x>2. Then
Question from the DSE 2006 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.