## ksaimouli 3 years ago optimization

1. ksaimouli

the sum of two non negative is 20 find the number if sum of their squares is larger as possible

2. ksaimouli

correct me if i go wrong @zzr0ck3r

3. ksaimouli

|dw:1352756469740:dw|

4. ksaimouli

thats all i get

5. ksaimouli

the sum of two non negative is 20 find the number if sum of their squares is larger as possible;as small as possible

6. ksaimouli

anybody there!!

7. ksaimouli

how to check the end points

8. ksaimouli

@henpen

9. ksaimouli

i got half problem

10. henpen

\[y=20-x\] \[y^2+x^2=400+2x^2-40x=M\]Maximise M

11. ksaimouli

how 400??

12. henpen

Do you want to minimise the square, as this doesn't have a maximum

13. henpen

\[(20-x)^2+x^2=400-20x-20x+x^2+x^2\]

14. ksaimouli

(a)

15. ksaimouli

ohh but i took derivative

16. henpen

Yes.

17. ksaimouli

i did not expand it instead did that

18. ksaimouli

x=10 is min but i need to check the end points too right but

19. ksaimouli

i dont get it

20. ksaimouli
21. ksaimouli

after x=10 what steps they did i did not understand

22. henpen

forget yahoo. |dw:1352759390040:dw| \[4x-40=0\] \[x=10\] \[y=20-10=10\] \[M_{min}=10^2+10^2=200\]

23. ksaimouli

i get min but i need max

24. henpen

|dw:1352759585039:dw|

25. ksaimouli

no but book answer shows 0 and 20

26. henpen

Actually, given that they have to be non negative there probably is a maximum

27. henpen

It's when y=20 and x=0

28. henpen

Geometrically it's obvious

29. henpen

Sorry, I wasn't thinking of the non-negatives only earlier

30. ksaimouli

ohh ok

31. ksaimouli

thx

32. henpen