anonymous 5 years ago Help!! I have no idea!

1. anonymous

2. anonymous

3. anonymous

see attached ^^^

4. anonymous

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

5. anonymous

no probs! I hope someone might

6. anonymous

the direction of the gradient is the direction of greatest increase

7. anonymous

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

8. anonymous

the magnitude of that vector is the greatest rate of change

9. anonymous

do you know how to find the partial derivatives?

10. anonymous

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

11. anonymous

fx= 2x +y fy = x

12. anonymous

?

13. amistre64

those look good for the gradient stuff

14. anonymous

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

15. anonymous

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

16. anonymous

don't I need a z point?

17. anonymous

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

18. anonymous

so the magnitdue is sqrt(2) ?

19. anonymous

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

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