Suppose f ( x, y ) = [x/y], P = ( −4, −1 ) and v = −2 I − 2 J.
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
C. Find the directional derivative of f at P in the direction of v, where the direction u of a vector v is the unit vector obtained by normalizing that vector, i.e., u = [(v )/(|| v || )].
Du f = ?
D. Find the maximum rate of change of f at P.
?
E. Find the (unit) direction vector in which the maximum rate of change occurs at P.
u = ? i + ? j

Question

Suppose f ( x, y ) = [x/y], P = ( −4, −1 ) and v = −2 I − 2 J.
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
C. Find the directional derivative of f at P in the direction of v, where the direction u of a vector v is the unit vector obtained by normalizing that vector, i.e., u = [(v )/(|| v || )]. 
Du f = ? 
D. Find the maximum rate of change of f at P. 
?
E. Find the (unit) direction vector in which the maximum rate of change occurs at P. 
u = ? i + ? j

turingtest · Answer

http://tutorial.math.lamar.edu/Classes/CalcIII/GradientVectorTangentPlane.aspx

turingtest · Answer

A: f(x,y)=x/y
partial w/respect to x is fx(x,y)=1/y i
partial w/respect to y is fy(x,y)=-1/(2y^2) j
(Del)f=(1/y)i-1/(2y^2)j
try B yourself first from here...