- #1
Punkyc7
- 420
- 0
find the directions in which the directional derivative of f(x,y)=x^2 + sin(xy) has a value of 1 at the point (1,0)
Fx=2x+ycos(xy)=2
Fy=xcos(xy)=1
So we have <2,1> and we need to find vectors that dotted with <2,1> =1
<2,1>.<x1,x2>=1
2x1+x2=1
So whn x1 is 0 we have x2 is 1
so one of the directions is <0,1>
im not sure how to find the other
Fx=2x+ycos(xy)=2
Fy=xcos(xy)=1
So we have <2,1> and we need to find vectors that dotted with <2,1> =1
<2,1>.<x1,x2>=1
2x1+x2=1
So whn x1 is 0 we have x2 is 1
so one of the directions is <0,1>
im not sure how to find the other