1. ## Stationary values

Show that $\displaystyle x\ln x$ has only one stationary value, and find it.

I differentiated the equation:
$\displaystyle \frac{d}{dx}(x\ln x) = x(\frac{1}{x})+ \ln x(1) = 1+\ln x$
Then
$\displaystyle 1+\ln x=0$
$\displaystyle \ln x=-1$
$\displaystyle x=e^{-1}=\frac{1}{e}$
Am i correct? Because the answer is supposed to be $\displaystyle -\frac{1}{e}$

2. Originally Posted by arze
Show that $\displaystyle x\ln x$ has only one stationary value, and find it.

I differentiated the equation:
$\displaystyle \frac{d}{dx}(x\ln x) = x(\frac{1}{x})+ \ln x(1) = 1+\ln x$
Then
$\displaystyle 1+\ln x=0$
$\displaystyle \ln x=-1$
$\displaystyle x=e^{-1}=\frac{1}{e}$
Am i correct? Because the answer is supposed to be $\displaystyle -\frac{1}{e}$
The x-coordinate of the stationary point is x = 1/e. However, the question is not asking for that value, it's asking for the value of the function. And that value is obviously found by substituting x = 1/e into the given rule ....

3. ok thanks! that was what i missed