Question

Find the absolute maxima and minima of the function on the given domain Tix. y) = x + xy .y? - 6x4 on the rectangular plate 0 sxs5 - 3sy so The absolute maximum occurs at (Type an ordered par) The absolute maximum is The absolute minimum occurs at (Type an ordered pait) The absolute minimum is Aflat circular plate has the shape of the regionxy s 1 The plate, including the boundary where x+y=1, is heated so that the temperature at the point (X.) is TOKY)=x+2y-X Find the temperatures at the hottest and coldest ponts on the plate degrees The hottest temperature on the plate is (Type an integer or a simplified fraction) The coldest temperature on the plate is (Type an integer or a simplified traction) degrees Find the point on the plane 5x + 2y + 2 = 8 that is nearest the origin What are the values of x, y, and z for the point? (Type integers or simplified fractions)

7-9 please. really having a hard time.

Answer 1

Sohetih T= Rryt maguler The fautcdary ffs buchglet s anly LEO Jaft side neo,-3y<o uhher sidk yeo, e<CE Jowrr Bide d3, osxef Gkulate fist adr darvadas af Te) Tyn+2y Th= 2nty-6 rxteal Bintsu, Tr 2nty-C0 2/lay 2nt ayo 271= C+2 Grthal font (t,-2) cS Scanned with CamScanner

Vehur ef the Anchn t t-2) b T =16-0+4-24 +t The ight sde s defind s n-,3y T TE,) = 25+2 ty-30 +4 y+Y-1 Finding the abslute extonof Te) en th nght lk is evalunt to frd the abshute extatne f H h the ge3Y So This nin the 1nye H-3 -15-1 = -7 H) = # -29 -25 Natica thet upiy dhfiniefish ef ), hee r aheg fandhin valu f To 2(3)= T(E,-S) -7 30340 Scanned with CS CamScanner

The eft side isno,-3y HOTOY 3)= T(o, -3)=13 0-TO0)= 4 HO) To,)= 4 The ufer sidk is , o h thenge Aov = 2n- ACo To) + TE,) T(3,) 3 4(3) -5 The Sauis Edh is 0 Aa T-3) = -3+9-tt = -gnt13 KW = 21-9 n-9% is inthe A0TO3)=13 h(E) TE-3) -7 h(%)= TV-3) = -25 CS Scanned with CamScanner

Collict all fthctin val of Tey) T(4,-2)=-8, TE3)7,T) = -1 TE,-5 TO) = 4, Te) = -5, T - -2 To-3)- 13 1 1 The abelt maximm occus t Phe abshte maximum is T3 The dbshe minimun cuts at, -2 The afehth minimm is T CS Scanned with CamScanner