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Math Help - hyperbolic problem!!stuck!!

  1. #1
    Member i_zz_y_ill's Avatar
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    Question hyperbolic problem!!stuck!!

    Q show curve y=cosh2x -10coshx+13 has three stat points and find y co-ord of stat points,,,

    i get (0,4) (-ln(6.25+(5.25)^0.5,-6.19) (ln(6.25+(5.25)^0.5,6.19)

    im using calc fx-9750 PLUS and the *** thing when i trace the stat points gives (0,4) and (-1.6,-0.5) and (1.6,0.5) so i concluded i must be wrong,,,,,,,does n e one know where ive gone wrong? previously useddouble angle cosh2x=2cosh^2x-1 then for y co-ords both expansion using cosh 2x=0.5(e^x etc and bunging in calc gave me 6.19)

    can some1 pls help!
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Upon differentiating, we can write the derivative in terms of e.

    f'(x)=(e^{x})^{2}-5e^{x}+\frac{5}{e^{x}}-\frac{1}{(e^{x})^{2}}

    Multiply through by e^{2x} to shed the fractions:

    e^{4x}-5e^{3x}+5e^{x}-1

    Now, you can let u=e^{x} and get:

    u^{4}-5u^{3}+5u-1=0

    Solving this we find the real solutions are u=-1, \;\ u=\frac{5-\sqrt{21}}{2}, \;\ u=1, \;\ u=\frac{\sqrt{21}+5}{2}

    Since  u=e^{x} we see the solutions are:

    x=ln(\frac{5-\sqrt{21}}{2}), \;\ x=0, \;\ x=ln(\frac{\sqrt{21}+5}{2})
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  3. #3
    Member i_zz_y_ill's Avatar
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    cheers but..

    thnx where did i go wrong with d/dx(cosh2x-10coshx+13)
    = 2sihx -10sinhx

    =0 using sinh2x=2sinhxcoshx

    4sinhxcoshx-10sinhx=0
    2sinhx(2coshx-5)=0
    sinhx=0 x=0 2coshx=5
    x=arcosh2.5
    x=+/- ln(6.25+(5.25^0.5) ??? ur method confused me when u^4 -5u^3 +5u -1=o
    i did u(U^3-5u^2+5)=1
    which gives u=1 not u=-1 then i think i do u^2(u-5)=-4
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  4. #4
    Member i_zz_y_ill's Avatar
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    Cheerz

    sorry i thin k i gotiot now thnx ill let u know if i go wrong later probs when i sub in CHEERS
    !!!!!!!!!!!!!!!!!
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