1. Find the directions in which the directional derivative of f(x,y)=x^2 + sin(xy) at the point (1,0) has value 1.
I tried to solve it, and I got the positive y direction for the answer. But I'm not sure if it's right or not.
Can anyone help with this problem?
2006-08-02 13:02:30 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
df/dx=2x+ycos(xy)
df/dy=xcos(xy)
Evaluated at (1,0) the components are (2,1)
So you want to find the unit vector which makes an inner product (dot product) of 1 with the vector (2,1).
This means that you want to solve
2cos(a)+1sin(a)=1
for the angle (a). Certainly the positive y direction works. Are there any other solutions? You also know that sin^2(a)+cos^2(a)=1, so you have two equations in two unknowns. Go to it!
2006-08-02 13:21:22 · answer #1 · answered by Benjamin N 4 · 0⤊ 3⤋