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)?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.
|
Solution: The answer is A
By a theorem, the direction of the maximum increase of a function f of two or three variables is the unit vector u in the direction of the gradient vector of f defined as,
At the point (1,1,0), the corresponding partial derivatives are:
Hence, the direction of maximum increase of f at the point (1,1,0) is,
