Question

Consider the function ?(?, ?) = ?³ + ?² + 4?? − 2.

1. Find all critical points of ?.

2. Use the Second Partials Test to determine whether each of the critical points of ? gives a relative maximum, relative minimum, or saddle point. You must clearly demonstrate your use the the Second Partials Test to determine the answer. Write your answers in the blanks below and then provide the specific information that you used to make your determination based on the Second Partials Test.

I conclude that the critical point _______________ gives a _______________________________________________ Reasoning:

I conclude that the critical point _______________ gives a _______________________________________________ Reasoning:

Answer 1

#my2= ~34 + 4му - So critical porut (0,0), (8,5) + (~19 г. x+ чу былу) = y + чи For critical point Fullylzo Fylniyleo (wmy )6 Туучу). 2 Тау (му) е - 3*+чу ? 29 + чи го де во сого) Timleo)= {to) - о Х2. 2. 3х24402 о Ях + 40 2 А и, о эх --Ви a Cзх-3), а Ғуу (4, 0) ту (зро) - 9 'D = Fru fyy ~ (Fry)" (9)2 1 = -16 го So Dco then rojo) is saddle г. 012-) о го 12 y=-2x 1920 At - B, 9. - coly -16 9+ - 3 port

Mt (9,-) Per la z 6(%) 16 10) 2 Z Fyyl! g) & Bny (,-4)4 2 Frun. Fyy -(fuy) D : Z 2 (4) 1618) Z z 32-16 Dz 1670 8 Emme (8,0)=le> 0 Sout (%, ; -18) relatre morninum

I conclude that the critical port (oo) is Saddle point because DCO I conclude that Goutral port (6,15,- ) point Is rebotine nunnum because cuse DTO forte (3,14970 Also There is no relative Maranum pont.