## AravindG 3 years ago find local maxima and local minima for the function f(x)=sin x-cos x 0<x<2

1. AravindG

@hartnn

2. uzumakhi

for this you have to find f'(x)

3. AravindG

ok ....cos x + sin x then?

4. uzumakhi

and then take f'(x)=0

5. AravindG

sin x+cos x=0

6. AravindG

sinx=-cos x

7. AravindG

nw what ?

8. uzumakhi

cos x + sin x = 0 cos x = -sinx

9. AravindG

k then ?

10. AravindG

why u delete that?

11. uzumakhi

find the value of x

12. AravindG

x=-pi/4 isnt it?

13. uzumakhi

no we have to take the value from 0 to 2

14. AravindG

then hw ??

15. uzumakhi

take x = 135 degrees

16. uzumakhi

17. AravindG

2.355

18. AravindG

x=3pi/4

19. hartnn

if x is between 0 to 2pi, then x= 3pi/4 is correct.

20. AravindG

k then hw we find local maxima and local minima ?

21. hartnn

local only means 'in that interval' , here 0 to 2pi

22. AravindG

so what are maxima and minima here ?

23. hartnn

so here u'll have only one value , at x=3pi/4 find f(x) when x=3pi/4

24. AravindG

also at x=7pi/4 we have only one value so f'(X)= ives 2 values for x isnt it?

25. AravindG

f'(X)=0 gives 2 values for x isnt it?

26. hartnn

oh yes! i missed that. now its even simpler..... find the second derivate, what u get ?

27. AravindG

-sinx +cos x

28. AravindG

whats the use of taking second derivative ?

29. hartnn

to know which point is max. or min. , u know how ?

30. AravindG

nop

31. AravindG

is it by substituting 3pi/4 and 7pi/4 in f''(X) and getting the sign to tell which is maxima and minima?

32. AravindG

k gt it !!!

33. hartnn

yes, if f''(x) > 0 , then max or min ?

34. hartnn

ok, good :)

35. AravindG

3pi/4 is max other is minima !!

36. AravindG

can u check up the answer for the next qn also ?

37. hartnn

sure ...

38. AravindG

i will post separately