Review 2 - at 30 mi/ hr. on roads that intersect at point...

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MA 242 REVIEW 2 Let F(x,y,z)= x 2 y 2 + z 3 x , P:(1,3,2) and u= < - 2 , 1 , 2 > . Find a. The rate of change in F at P in the v direction. b. The gradient of F at P. c. The direction of max. increase in F at P. d. The max. increase in F at P. e. The equations of the tangent plane and normal line to x 2 y 2 + z 3 x = 17 at P II. Find the equation to the tangent line of the curve of intersection to F(x,y,z) = xy + z 2 = 3 and G(x,y,z)= xz 2 - y 3 = 0 at P:(1,1,1). III. Find max - min - saddles for: a. f ( x, y ) = x 3 - 12 x + y 3 + 3 y 2 b. f ( x, y ) = x 3 + 3 y 2 - 3 xy IV. Car A is moving due south at 20 mi/hr and car B is moving due east
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Unformatted text preview: at 30 mi/ hr. on roads that intersect at point P. If A is 4 mi north of P and B is 3 mi west of P, how fast is the distace between them changing? V. Find the absolute max and min for f(x,y)= x 2 + y 2-2 x-2 y on the region bounded by y=0, x= 4 and y=2x. VI. Let z = f ( x, y ) = x 2 y + y/x, x = uv and y = u 2 + v 2 . Find a. f v b. f v at (u,v) = ( 2, 3) 1...
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