1. Let f(x,y,z) = e^{xyz} + ln(1 + x^{2} + y^{2} + z^{2}) 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) = (x^{2} + y^{2})^{-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)/(x^{2}+y^{2})^{3/4}] |
C. 1/(x^{2}+y^{2})^{3/2} |
D. (1/2)[(x+y)/(x^{2}+y^{2})] |
E. 1/(x^{2}+y^{2}) |
3. What is the directional derivative of f(x,y) = 4x^{2}y^{4} - 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 - 4x^{2} - 3y at (x,y) toward (0,0)?
A. -8x - 3 |
B. (-8x^{2}-3y)/(x^{2}+y^{2})^{1/2} |
C. (-8x-3)/(64x^{2}+9)^{1/2} |
D. 8x^{2} + 3y |
E. (8x^{2}+3y)/(x^{2}+y^{2})^{1/2} |