Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
icon
Related questions
Question
Are the following functions quasi-concave? Assume x ≥ 0
a) f(x) = a
b) f(x) = a + cx²,c<0
Are the following functions quasiconcave, quasiconvex, both, or neither:
a) f(x) = x³ - 2x
b) f(x₁, x₂) = 6x₁ - 9x2
c)
f(x₁, x₂) = x₂ - In x₁
d) f(x,y) = (x + 1)²-(y + 2)² for x,y > 0
Transcribed Image Text:Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx²,c<0 Are the following functions quasiconcave, quasiconvex, both, or neither: a) f(x) = x³ - 2x b) f(x₁, x₂) = 6x₁ - 9x2 c) f(x₁, x₂) = x₂ - In x₁ d) f(x,y) = (x + 1)²-(y + 2)² for x,y > 0
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage