Question

Help!! I have no idea!

Answer 1

whatd your question?

Answer 2

see attached ^^^

Answer 3

i just did and ummmm im not very sure about it sorry:(

Answer 4

no probs! I hope someone might

Answer 5

the direction of the gradient is the direction of greatest increase

Answer 6

so take (dF/dx,dF/dy) at the point (-1,1) and that vector points in the direction of greatest increase

Answer 7

the magnitude of that vector is the greatest rate of change

Answer 8

do you know how to find the partial derivatives?

Answer 9

yes, sorry I'm doing work at the same time

Answer 10

fx= 2x +y
fy = x

Answer 11

?

Answer 12

those look good for the gradient stuff

Answer 13

yep they are right, now evaluate the derivatives at the specified point and you have the gradient vector. Then you can find magnitude.

Answer 14

so eval at (-1,1) fx=-1 fy =-1

Answer 15

don't I need a z point?

Answer 16

magnitude is \sqrt((a_1)^2 + (a_2)^2) so I use the -1,-1 ?

Answer 17

so the magnitdue is sqrt(2) ?

Answer 18

\[<-1/\sqrt{2}, 1/\sqrt{2}>\]