dabears900 4 years ago Help!! I have no idea!

1. dabears900

2. animalsavior94

3. dabears900

see attached ^^^

4. animalsavior94

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

5. dabears900

no probs! I hope someone might

6. rsvitale

the direction of the gradient is the direction of greatest increase

7. rsvitale

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

8. rsvitale

the magnitude of that vector is the greatest rate of change

9. rsvitale

do you know how to find the partial derivatives?

10. dabears900

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

11. dabears900

fx= 2x +y fy = x

12. dabears900

?

13. amistre64

those look good for the gradient stuff

14. rsvitale

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

15. dabears900

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

16. dabears900

don't I need a z point?

17. dabears900

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

18. dabears900

so the magnitdue is sqrt(2) ?

19. chaguanas

$<-1/\sqrt{2}, 1/\sqrt{2}>$