|
A.
|
B.
|
C.
|
|
D.
|
E.
|
1. Let f(x,y,z) = exyz + ln(1 + x2 + y2 + z2) where x,y,z are real numbers. What is the direction of maximum increase of f at the point (1,1,0)?
|
A.
|
B.
|
C.
|
|
D.
|
E.
|
2. Let f(x,y) = (x2 + y2)-1/2 for (x,y) not equal to zero. What is the directional derivative of f at the point (x,y) in the direction toward the origin?
|
A. 1 |
B. (1/2)[(x+y)/(x2+y2)3/4] |
C. 1/(x2+y2)3/2 |
|
D. (1/2)[(x+y)/(x2+y2)] |
E. 1/(x2+y2) |
3. What is the directional derivative of f(x,y) = 4x2y4 - 2x + 5 at the point (2,1) in the direction <-3,4>?
|
A. -136/5 |
B. 107/[2(1073)1/2] |
C. 160/7 |
|
D. 214/5 |
E. 214 |
4. What is the directional derivative of f(x,y) = 5 - 4x2 - 3y at (x,y) toward (0,0)?
|
A. -8x - 3 |
B. (-8x2-3y)/(x2+y2)1/2 |
C. (-8x-3)/(64x2+9)1/2 |
|
D. 8x2 + 3y |
E. (8x2+3y)/(x2+y2)1/2 |
