b. Define f:R2→R by f(x1​,x2​)=x12​+2x1​−5x2​+x22​−6 i. Find the critical points. ii. Classify those critical points. ii

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B Define F R2 R By F X1 X2 X12 2x1 5x2 X22 6 I Find The Critical Points Ii Classify Those Critical Points Ii 1 (33.49 KiB) Viewed 29 times

b. Define f:R2→R by f(x1​,x2​)=x12​+2x1​−5x2​+x22​−6 i. Find the critical points. ii. Classify those critical points. iii. Find the minimum value of f(x1​,x2​) subject to the constraint x+y=7. i. Find the minimum value of f(x1​,x2​) subject to the constraint x+y=7 c. Check whether the given functions are conwex or not. 1. f(x,y)=x2+2xy−y2 2. g(x,y,zˉ)=x2+y2+z2−xyz d. Find the global maximum/ minimum of f(x,y)=x3−12x+5, −6≤x≤+6. Then determine the local maximum/ minimum. 4 2. Show that any field line of the given vector field F(x,y)=(−2ℏ​y,x) is a circle centred on the (2,0). b. Find the equations of tangent plane and the normal line to the surface at the point (1,2,0),2x2−y2+3xz=0 c. Compute the directional derivative of φ=x2z+2xy2+yz2 at the point (1,2,−1) in the direction of the vector A=2i+3j−4k. 5. 2. Consider parametric equations x=4t,y=2t2,z=4+t [t any real numeber]. Find the coordinate points for t=−1,−21​,0,21​,1. b. Evaluate ∫c​Fd r, from (2,0) to (0,2) where F=2x2i+3yj along. i. c=c4​ : the straight line between (2,0) and (0,2). ii. c=c2​ : the quarter circles centred at the origin with the radius 2