## lilly21 2 years ago locate the absolute extrema of the function (if any exist) over the interval. f(x)=2x-3 [0, 2]

1. infoshark

Familiar with the derivative ? can you take the derivative of f(x), if so, what do you get ?

2. lilly21

2

3. infoshark

what are the roots of 2 ? where does it cross the x axis

4. lilly21

at y=0???

5. infoshark

can y ever be zero if it always equals 2 ?

6. lilly21

nope

7. infoshark

any max extrema then ?

8. infoshark

abs*

9. lilly21

im kinda of confused by ur question :[

10. hartnn

u got x=2 put it in f(x) to find the extrema

11. lilly21

1 ?

12. hartnn

thats correct :)

13. lilly21

thats it?

14. hartnn

wait. for extrema, u take derivative and equate it to 0 means you do, f'(x)=0 but you got f'(x) = 2 hence there is no extrema.....

15. lilly21

but you c in my book it has an answer or answers of min (0,-3) and max (2,1)

16. hartnn

i know, there is no global extrema, and so, here we find local extrema by substituting the endpoints. so put x=0 and x=2 and find f(x)

17. hartnn

*local = absolute

18. hartnn

whenever we don't get global extrema, we put endpoints....remember this.

19. lilly21

i am utterly confused :[

20. hartnn

lets start over ?

21. lilly21

22. hartnn

ok, absolute extrema means max or min points in the given interval.

23. hartnn

now to find min or max values, you take derivative of function and set it =0

24. hartnn

then you get values of x for which the function is min/max. if f'(x) cannot be equal to 0, then there is no global extrema ok ?

25. lilly21

ok

26. lilly21

or if its like 1/0 right?

27. hartnn

in that case, we can find 'local' or 'absolute' values at the endpoints, they become min/max values.

28. hartnn

yes.

29. lilly21

so 2=0

30. hartnn

i can't think of an example when u get 1/0 after taking the derivative.

31. hartnn

here , you get f'(x) =2 we cannot equate this to 0

32. hartnn

because 2 can never =0 hence there is no extrema, or as we say, no global extrema

33. hartnn

but we can find absolute extrema, that is min/max in GIVEN INTERVAL

34. lilly21

how do we find these?

35. hartnn

one of the end-point is x=2 there what is f(x) = ?

36. lilly21

1?

37. hartnn

so the point is (2,1) and this is one of the extrema we don't know yet whether this is max or min

38. hartnn

now put other end point, x=0 what is f(x)

39. lilly21

wait where did we get x=0?

40. hartnn

[0,2]

41. jaersyn

42. hartnn

thats where i got x=2 also earlier

43. lilly21

ooooooooo okay there will be 3 extrema right???

44. hartnn

how come 3 ? one for x=2, and one for x=0

45. lilly21

o yeah my bad -_- :]

46. lilly21

we do the same for 0 right ???? plug it into the orig equation? right?

47. jaersyn

you could just say there's no global min/max since the function is linear right?..

48. hartnn

yes.

49. hartnn

to both

50. jaersyn

k, thanks. double checking.

51. hartnn

now put other end point, x=0 what is f(x)

52. lilly21

-3?

53. hartnn

so the other point is ?

54. hartnn

and which one should be min and which one should be max ?

55. lilly21

0,-3 is min the other is max?

56. hartnn

yes, thats correct. clear with every step ?

57. lilly21

yes sir or mam! :]

58. lilly21

thanks so much!

59. hartnn