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AravindG

  • 3 years ago

find local maxima and local minima for the function f(x)=sin x-cos x 0<x<2

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  1. AravindG
    • 3 years ago
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    @hartnn

  2. uzumakhi
    • 3 years ago
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    for this you have to find f'(x)

  3. AravindG
    • 3 years ago
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    ok ....cos x + sin x then?

  4. uzumakhi
    • 3 years ago
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    and then take f'(x)=0

  5. AravindG
    • 3 years ago
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    sin x+cos x=0

  6. AravindG
    • 3 years ago
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    sinx=-cos x

  7. AravindG
    • 3 years ago
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    nw what ?

  8. uzumakhi
    • 3 years ago
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    cos x + sin x = 0 cos x = -sinx

  9. AravindG
    • 3 years ago
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    k then ?

  10. AravindG
    • 3 years ago
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    why u delete that?

  11. uzumakhi
    • 3 years ago
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    find the value of x

  12. AravindG
    • 3 years ago
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    x=-pi/4 isnt it?

  13. uzumakhi
    • 3 years ago
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    no we have to take the value from 0 to 2

  14. AravindG
    • 3 years ago
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    then hw ??

  15. uzumakhi
    • 3 years ago
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    take x = 135 degrees

  16. uzumakhi
    • 3 years ago
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    convert it to radians

  17. AravindG
    • 3 years ago
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    2.355

  18. AravindG
    • 3 years ago
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    x=3pi/4

  19. hartnn
    • 3 years ago
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    if x is between 0 to 2pi, then x= 3pi/4 is correct.

  20. AravindG
    • 3 years ago
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    k then hw we find local maxima and local minima ?

  21. hartnn
    • 3 years ago
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    local only means 'in that interval' , here 0 to 2pi

  22. AravindG
    • 3 years ago
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    so what are maxima and minima here ?

  23. hartnn
    • 3 years ago
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    so here u'll have only one value , at x=3pi/4 find f(x) when x=3pi/4

  24. AravindG
    • 3 years ago
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    also at x=7pi/4 we have only one value so f'(X)= ives 2 values for x isnt it?

  25. AravindG
    • 3 years ago
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    f'(X)=0 gives 2 values for x isnt it?

  26. hartnn
    • 3 years ago
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    oh yes! i missed that. now its even simpler..... find the second derivate, what u get ?

  27. AravindG
    • 3 years ago
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    -sinx +cos x

  28. AravindG
    • 3 years ago
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    whats the use of taking second derivative ?

  29. hartnn
    • 3 years ago
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    to know which point is max. or min. , u know how ?

  30. AravindG
    • 3 years ago
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    nop

  31. AravindG
    • 3 years ago
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    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
    • 3 years ago
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    k gt it !!!

  33. hartnn
    • 3 years ago
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    yes, if f''(x) > 0 , then max or min ?

  34. hartnn
    • 3 years ago
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    ok, good :)

  35. AravindG
    • 3 years ago
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    3pi/4 is max other is minima !!

  36. AravindG
    • 3 years ago
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    can u check up the answer for the next qn also ?

  37. hartnn
    • 3 years ago
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    sure ...

  38. AravindG
    • 3 years ago
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    i will post separately

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