Hey can you help me my homework Please show and organize your work clearly. I finish 70- 90% of the work you just have to finish the work.

100ry G. The temperature at any point (r, y) in the ry plane is given by T = Find the directional derivative at the point (2. 1) in a direction making an angle of 60" with the positive r-axis. 7. In the problem 6.), In what direction from (2, 1) would the derivative be a maximum? What is the value of this maximum? 8. Find the equation of the tangent plane to the surface r'ty' = 42 at the point (2, -4, 5). 9. A rectangular box, open at the top, is to have a volume of 32 cubic feet. What must be the dimensions so that the total surface area is a minimum? 10. Find the maximum and minimum values of the function f(x,y) = r ty subject to the condition ar'+ 4ry + 6y' = 140.$ ( - 12 ) ( # ) + ( ? ) ( 12 ) = ? 7 ( 2) D - On+T Will be max If Z wed The same direction The max Value of DOT . = [ 7 ?8 eq of the tangent Plane Riveow 1 if the surface even by the grivee of the fuction z = f ( x,Y ) eq the tangent plane of cxox 2 - to -. - of exoIYOTED ( X - XO ).+ Jy 1 x 2 + x t y z = y z v z = y of = I(X , Y ) 5X 4 3 X at ( 2 , - 4, 5 ) of = 1 of = 1 OX 2 of = - 2 ay 2 - 5 = 1 . ( x = ) + ( - 3 ) ( y - )X y Z = 0f ( x y ) = X - yz D max / min 3 x 2 + 4 x y + by 2 140 = 0 g ( x, y ) + has max /min at (x,yl - D There eants X ER V f = 209 hint ( z X = > ( G X + 4 4 ) 2 4 = 2 ( 12 4 + 4x ) solvefor 3 x 2 + 4 x 4 7 6 y z = 140( 61 - 2 ) x + q x 4 = solve for 4 x x + ( 12 x - 2) X1y 3 x 2 + 4 x y + 6 y R = 1 4 0 (and A )Ay JK 6 10oxy 60 T( x y ) = x 2 + 42 (2, 1) at ( 2 , 1 ) 2 Review Direchiand ' u but C xy) = I f. it of bay ) J E ( x , y ) u , + zy 2 x The Unit Vector W = W = D T ( 2 , 1 ) F + ( 2 , 1 ) - 4 =