Classify the following functions with respect to concavity and convexity. Please explain as detailed as possible, step by step. a) f(x)=2x4−8x2+3 ; b) f(x,y) = (x2+y2)1/3 ; c) f(x,y) = (2x2−3xy+5y2)3 + x2+4y2+2x−5y+3 ; d) f(x,y)=ex+ey−x−y ; e) f(x,y)=log(xy) ; f ) f(x,y) = 3x2−7xy+4y2 ; g) f(x,y,z)=zy2z3 ; h) T(p,q,r)=p3r+q3r−5r en D = {(p, q, r) ∈ R3 | p > 0, q > 0, r > 0} ; i ) g(u, v,w) = uln(vw) enD = {(u, v,w) ∈ R3 | u > 0, v > 0,w > 0}.

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Answered: Classify the following functions with…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 36E

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Classify the following functions with respect to concavity and convexity. Please explain as detailed as possible, step by step. a) f(x)=2x⁴−8x²+3 ; b) f(x,y) = (x²+y²)^{1/3 ;}c) f(x,y) = (2x²−3xy+5y²)³ + x²+4y²+2x−5y+3 ;
d) f(x,y)=e^x+e^y−x−y ; e) f(x,y)=log(xy) ; f ) f(x,y) = 3x²−7xy+4y² ; g) f(x,y,z)=zy²z³ ; h) T(p,q,r)=p³r+q³r−5r en D = {(p, q, r) ∈ R³ | p > 0, q > 0, r > 0} ; i ) g(u, v,w) = uln(vw) enD = {(u, v,w) ∈ R³ | u > 0, v > 0,w > 0}.