Identify the x-coordinate of any relative extrema of y = xln(x) , I know the answer need an explanation on approach thanks

Question

Identify the x-coordinate of any relative extrema of y = xln(x) ,    I know the answer need an explanation on approach thanks

anonymous · Answer

is it 1/e??

anonymous · Answer

Relative min at x = 1/e

anonymous · Answer

yeah, how can u get the maxima here??

asnaseer · Answer

you need to differentiate the function and then work out what value of x will it zero.

asnaseer · Answer

*will make it

asnaseer · Answer

@frank545 - do you know how to differentiate this function?

slaaibak · Answer

derivative using chain rule:

f'(x) = x * 1/x + lnx = 1 + lnx

1 + lnx = 0

ln x = -1 

x=e^-1=1/e

anonymous · Answer

Yes I understand differentiation, I was looking for a theoretical explanation in terms of what i look for when finding relative extrema

asnaseer · Answer

the differential define the slope of the tangent line to the curve

asnaseer · Answer

at a relative extrema, the slope is horizontal, and therefore equal to zero

asnaseer · Answer

e.g. look at this sample graph:
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