1. ## 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!

2. Upon differentiating, we can write the derivative in terms of e.

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

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

$\displaystyle e^{4x}-5e^{3x}+5e^{x}-1$

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

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

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

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

$\displaystyle x=ln(\frac{5-\sqrt{21}}{2}), \;\ x=0, \;\ x=ln(\frac{\sqrt{21}+5}{2})$

3. ## 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

4. ## Cheerz

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