Stationary point of s(t)=t lnt (Maths).

[_Imwashingmypirate]

Hey I am working on a question and am stuck. I differentiates the equation in the title to get; lnt +1

lnt+1=0 (For stationary points).

e^(lnt) = e^(-1)

t=1/e

I now want to find y. I put this back into the equation...

y = 1/e ln (1/e)

Do I put these together to get, y = ln/e^2 Or am I on another planet. How do I find y?

Thanks,

[_Imwashingmypirate]

Or do I use product rule? If so then do I take t = u, ln = v and t=w?

[_Dr. Shades]

You do both.

[_Imwashingmypirate]

Erm Ok. Thanks.

[_Imwashingmypirate]

Actually it's all wrong above. I worked it out.

[_asbestosman]

Actually it's all wrong above. I worked it out.

t=e ?

proof:
t = s(t)
t = t *ln(t)
1 = ln(t)
e^1 = t

[_Imwashingmypirate]

t = 1/e any s = -1/t

Proof



s(t)=t lnt

s' = lnt +1

lnt+1=0 (For stationary points).

lnt = -1

e^(lnt) = e^(-1)

t=1/e

I now want to find y. I put this back into the equation...

y = tlnt

t = 1/e
lnt = -1 from above.

therefore tlnt = -1/e

thus s = -1/e

Resulting in the stationary point of s(t)=tlnt, being (1/e, -1/e)