Math 32A hw 7

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nw 7 1. f(x,y) xy2 3r(t) (2 t2 + 3) 4. let f(x,y) xe*Y and P (3,9) angle of 45. Of (y2,2xy) r'(t) (t,3t27 calc 11pH): fx(x,y) (2x 2 1)cex *) fy(x,y) - xex - 3 use chain rule to evaluate of (r(t) @ t = 1.5 Vfp ((2(3) 1)(e32 q). (z)e 4-((2.9 1)(ei), -3e7 (19,-3) frc + ) "f(rce): ((t)2,22t2.-37 (+4, + 5) f(x) v'(t) (tY + 5).(t,3t2y + 3 t (1.5) + 3(1.5) = 68.344 use chain rule to evaluate f(r(+1) &t = -1.8 sin,tic. St,xthy: t4+ 19: caissigs: -213668 s. in man in 2. calculate the gradient g(x,y)- y fy(0,10,21) 0 cOS (0 2i) 0 axos y ei ? 09 & f(x) axg(x) xxy2 x 9x 2x Duf(p): 118 fall cosO Not(cosso): Fo() = -g (ie, ch 9. 1 *5 = - 31 ** - 44 x 5 28 3. Calculate the gradient h(x,y,2) xyz7 -n (yz,xz , xxyz 87 of y - 2x 32( 2x) + x 6( 2x) 3) 2x)2 0 m(t) = (v l)' fz(0,10,21) = (OS 10 21) 1 6. find a fan f(x,y, 2) such they of is the constant rector (2,3,22 10.2 inning x -x 7e7x 6 3eby 2e z f(x,y,z) 7x 3y 2z C 12. f(x,y 7. find the critical points of f(x,y) 8y" x2 xy 3y2 y3 (3y 4)(y b) 0rzy - 4x y - 43,6 fx 2x y 0 fy 32y3 by 3y2 x 0 into """ e 2564 x 12x 12x2 + 256x3 12x2 + 13x - 12( - Y3) + 28 = 44703fxx = 2 - local max x(- 256x2 12x 13) 0 - x 0 x 4x = for y-c00r e -210) 0, 2(1) =, -2(5) 22 13. find crit points of fxn f(x,y) x + 2y24y + 2 x g(x,y) x2 -16xy y (0,0) (- , ) (,) AC - B use the 2nd derivative test to determine local min, max, I saddle fxx 2 fxy 1 fyy = 96y2 - by 6 - = 2x 20x - 1 -y 4y 4 = y 1 (-1,1) & (0,0) & (- i,) 09 8 - 16x 1 0x ib est, in a road an his is in an e sit, is