Suppose f(x,y)=x/y, P=(0,−1) and v=3i+3j. A. Find the gradient of f. ∇f= ____i+____j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇f)(P)= ____i+____j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf=? Note: Your answer should be a number D. Find the maximum rate of change of f at P. maximum rate of change of f at P=? Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u= ____i+____j Note: Your answers should be numbers
Suppose f(x,y)=x/y, P=(0,−1) and v=3i+3j.
A. Find the gradient of f.
∇f= ____i+____j
Note: Your answers should be expressions of x and y; e.g. "3x - 4y"
B. Find the gradient of f at the point P.
(∇f)(P)= ____i+____j
Note: Your answers should be numbers
C. Find the directional derivative of f at P in the direction of v.
Duf=?
Note: Your answer should be a number
D. Find the maximum rate of change of f at P.
maximum rate of change of f at P=?
Note: Your answer should be a number
E. Find the (unit) direction
u= ____i+____j
Note: Your answers should be numbers
Given that , and
(a) The gradient of f is
(b) The gradient of f at the point is
Answer :
(c) The Unit vector in the direction of the vector is
Now the directional derivative of f in the direction of the vector v at the point P is
The directional derivative of f in the direction of the vector v at the point P is
Answer :
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