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Questions › CUET-PG › CUET-PG 2023 Shift 1 › Q28
4 marks, −1Mathematics › Concavity, convexity and quasi-concavity › Convex sets and functionsModerateabout 1 min

CUET-PG 2023 Shift 1 Question 28: Concavity, convexity and quasi-concavity

A function is strictly concave in the interval I, if for all a,b∈Ia, b \in Ia,b∈I and λ∈(0,1)\lambda \in (0, 1)λ∈(0,1)

  1. f[(1−λ)a+λb]>(1−λ)f(a)+λf(b)f[(1-\lambda)a + \lambda b] > (1-\lambda)f(a) + \lambda f(b)f[(1−λ)a+λb]>(1−λ)f(a)+λf(b)
  2. f[(1−λ)a+λb]<(1−λ)f(a)+λf(b)f[(1-\lambda)a + \lambda b] < (1-\lambda)f(a) + \lambda f(b)f[(1−λ)a+λb]<(1−λ)f(a)+λf(b)
  3. f[(1−λ)a+λb]≥(1−λ)f(a)+λf(b)f[(1-\lambda)a + \lambda b] \geq (1-\lambda)f(a) + \lambda f(b)f[(1−λ)a+λb]≥(1−λ)f(a)+λf(b)
  4. f[(1−λ)a+λb]≤(1−λ)f(a)+λf(b)f[(1-\lambda)a + \lambda b] \leq (1-\lambda)f(a) + \lambda f(b)f[(1−λ)a+λb]≤(1−λ)f(a)+λf(b)

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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. f[(1-λ)a + λ b] ≥ (1-λ)f(a) + λ f(b) 4. f[(1-λ)a + λ b] ≤ (1-λ)f(a) + λ f(b) (A) f[(1-λ)a + λ b] > (1-λ)f(a) + λ f(b) (B) f[(1-λ)a + λ b] < (1-λ)f(a) + λ f(b) (C) f[(1-λ)a + λ b] ≥ (1-λ)f(a) + λ f(b) (D) f[(1-λ)a + λ b] ≤ (1-λ)f(a) + λ f(b)

Also written as: A function is strictly concave in the interval I, if for all a, b in I and lambda in (0, 1) 1. f[(1-lambda)a + lambda b] > (1-lambda)f(a) + lambda f(b) 2. f[(1-lambda)a + lambda b] < (1-lambda)f(a) + lambda f(b) 3. f[(1-lambda)a + lambda b] >= (1-lambda)f(a) + lambda f(b) 4. f[(1-lambda)a + lambda b] <= (1-lambda)f(a) + lambda f(b)

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.

TestStop has 14 past-paper questions on this subtopic.

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