Math 27~ Page 5
10. The directional derivative of f{x,y,z) = xyz at the point (1,2,3) in
the direction from (1 , 2,3) toward (3 , 3,1) is
a) 1/4 b) 11
3 c) 19 d) 13
7
e) 17
6
11. By determining and testing the critical points of f{x,y)
we find that this function has
3 3
x - 3xy + Y ,
a) no critical points
b) a local minimum at (1,1) and a local maximum at (-1, -1)
c) a saddle point at (O,O) and a local minimum at (1,1)
d) a local minimum at (O,O) and a local maximum at (-1 , -1)
e) a saddle point at (1,1) only
12 . Suppose we wish to evaluate the iterated integral
2 1 3
f f x
ye dxdy.
0 y/2
If we reverse the order of integra ti on we have
1 2x 3 1 2 3
a) j j x dydx c) J j x
ye ye dydx
a 0 y/2 0
1 2 3 2 y/2 3
b) J J x dydx d) J J x
ye ye dydx
a 0 0 0
~, ~
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Math 27~ Page 5 10. The directional derivative of f{x,y,z) = xyz at the point (1,2,3) in the direction from (1 ,2,3) toward (3 ,3,1) is 13 11 e) 17 a) b) c) 19 d) 1/4 3 7 6 3 3 x - 3xy + Y , 11. By determining and testing the critical points of f{x,y) we find that this function has a) no critical points b) a local minimum at (1,1) and a local maximum at (-1, -1) c) a saddle point at (O,O) and a local minimum at (1,1) d) a local minimum at (O,O) and a local maximum at (-1 , -1) e) a saddle point at (1,1) only integral evaluate the iterated Suppose we wish to 12 . 2 1 3 x ye dxdy. f f 0 y/2 integra ti on we have reverse the order of If we 1 2 3 1 2x 3 x x ye dydx c) j ye dydx a) j j J y/2 0 a 0 y/2 3 2 2 3 1 x x dydx ye ye dydx d) b) J J J J 0 0 a 0 ~, ~~ ......... ...... 4' +-h,,", .." h .... ~yC>.