Complex Differentiation Watch

SimonHackland
Badges: 0
Rep:
?
#1
Report Thread starter 5 years ago
#1
Any help with this question would be highly appreciated,

Find the x-coordinates of the stationary points of
y=x^3 e^-kx, where k is a positive constant.

Thanks
0
reply
Khallil
Badges: 13
Rep:
?
#2
Report 5 years ago
#2
Have you encountered the product and chain rules of differentiation yet?

\dfrac{d}{dx} \left( u(x) \cdot v(x) \right) = u'(x) \cdot v(x) + u(x) \cdot v'(x)
0
reply
SimonHackland
Badges: 0
Rep:
?
#3
Report Thread starter 5 years ago
#3
(Original post by Khallil)
Have you encountered the product and chain rules of differentiation yet?

\dfrac{d}{dx} \left( u(x) \cdot v(x) \right) = u'(x) \cdot v(x) + u(x) \cdot v'(x)
I have used the product rule to get to this stage,

dy/dx=x^3(-ke^-kx)+e^-kx(3x^2)

I am unsure what to do from now onwards
0
reply
Khallil
Badges: 13
Rep:
?
#4
Report 5 years ago
#4
(Original post by SimonHackland)
I have used the product rule to get to this stage,

dy/dx=x^3(-ke^-kx)+e^-kx(3x^2)

I am unsure what to do from now onwards
Stationary points occur when the derivative of a function is 0.

You should also note that \forall x : e^{kx} \neq 0 so you can factor that out and omit it since it doesn't have any real solutions.
0
reply
SimonHackland
Badges: 0
Rep:
?
#5
Report Thread starter 5 years ago
#5
I have done it now, thanks for the help
0
reply
lubus
Badges: 11
Rep:
?
#6
Report 5 years ago
#6
(Original post by SimonHackland)
I have done it know, thanks for the help

*now
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Imperial College London
    Undergraduate Open Day Undergraduate
    Wed, 26 Jun '19
  • University of Brighton
    Photography MA open afternoon Postgraduate
    Wed, 26 Jun '19
  • University of Plymouth
    General Open Day Undergraduate
    Wed, 26 Jun '19

Who do you think will be the next PM?

Boris Johnson (229)
72.24%
Jeremy Hunt (88)
27.76%

Watched Threads

View All