Question

Let f(x,y) = 2x2 - 4x + y2 - 4y +1. 1) The number of critical points of f is: a. 0 b. 1 c. 2 d. 3 Оа. Ob. Ос. Od 2) The point (1,2) is: a. a local maximum forf b. a local minimum forf a saddle point for c. Оа. Ob Oc.

Answer 1

Solution on sall = 2 KEL -4 = 0 = 2 one when we given f(x, y) = 28²4x + y²uyt fx(x,y) = 442-4 fj crry)= 24-4 and fxx (x, y)=4 fay=c foy (x,y)=2 Cuitical points occur when Fe(x,y)=0 y Le-4=0 fy (x,y)=0 a 27-4 situation critical ger point at (xiy) = (1,2) critical point that is (1,2). then option is couiect option: 0 (0,0) = freul 01, b) fagra, b) - [ fwy (a,b)]* D(a,b)= 4.2-(0)2 DL1,2) = and if DC1, 2) >0 faal 1, 2) >0 then f has a local minimum at (1,2) that means means oprion is is couect option. gn het f= S. ' secer) dy dx (1,1) solving S' (secck) – Sec(K) .x) dx Here we get on 8. on we get I- fa 055065 1 15 here, option 6 corect oferion,

the all I = S. Sec(x) S da we - x By reversing order of Inregration dy get s pot sec x) dx dy opnion. - Hence, option (b is correct Solved.