Suppose f(x,y)=2x^2+2xy1y^2, P=(1,1), and u =1517,817. A. Compute the gradient o
ID: 2849466 • Letter: S
Question
Suppose f(x,y)=2x^2+2xy1y^2, P=(1,1), and u =1517,817.
A. Compute the gradient of f.
f(x,y)= i+ j
Note: Your answers should be expressions of x and y; e.g. "3x4y"
B. Compute the directional derivative of f in the direction of u .
Du f(x,y)=
Note: Your answer should be an expression of x and y; e.g. "3x4y"
C. Evaluate the gradient at the point P.
f(1,1)= i+ j
Note: Your answers should be numbers
D. Compute the directional derivative of f at P in the direction u .
Du f(1,1)=
Note: Your answer should be a number
Explanation / Answer
f(x,y)=2x2+2xy1y2
A. Compute the gradient of f.
fx=-4x+2y,fy=2x-2y
f(x,y)=<-4x+2y,2x-2y>
B. Compute the directional derivative of f in the direction of u .
Du f(x,y)=f. u/|u|
=<-4x+2y,2x-2y>.1517,817/[(1517)2 +(817)2]
=[1517(-4x+2y) + 817(2x-2y)]/1723
=[7702x -4668y]//1723
=4.47x-2.71y
C. Evaluate the gradient at the point P.
f(1,1)=<-4+2,2-2>=<-2,0>
D. Compute the directional derivative of f at P in the direction u .
Du f(1,1)=4.47-2.71=1.76