Stationary point of y = xlnx

[Monkeyseat]

Hi,

Question: Find the coordinates of the stationary point of the curve y = xlnx, leaving your answer in terms of e.

So I differentiated it and got dy/dx = 1 + lnx

Stationary point when dy/dx = 0 so:

1 + lnx = 0
lnx = -1
x = e^-1
x = 1/e

Okay, so to find y, I sub x back in.

When x = 1/e, y = (1/e)ln(1/e).

This is where I'm stuck. I can't get that fully simplified in terms of e. I know it is equal to:

y = ln((1/e)^(1/e))

But I don't know where to go now. Any suggestions? I know the answer is y = -1/e but I can't prove it from y = (1/e)ln(1/e).

Thanks.

 

[skeeter]

ln(1/e) = ln(1) - ln(e) = 0 - 1 = -1

help any?

 

[Monkeyseat]

ln(1/e) = ln(1) - ln(e) = 0 - 1 = -1

help any?

Ah, got it!

So:

y = (1/e)ln(/e)

Becomes (1/e) * (-1) = -1/e.

Thanks!