Another wrong question (well i think) (1 Viewer)

[sasquatch]

I just need verification. The question asks: Show that the miniumum value of y = x log x is -1/e.

dy/dx = log x + x * 1/x
= log x + 1

When dy/dx = 0

log x = -1
e^{log x} = e^-1
x = 1/e (no minus sign)

d²y/dx² = 1/x

So x has to be positive for a turning point to be a minimum (as d²y/dx² > 0 only when x > 0).

So this question is wrong?

EDIT: the y-coordinate at this point is -1/e, so when it asks for the minimum value, does that refer to minimum y-value then?

 

[Riviet]

Remember that the min/max value refers to the y-coordinate of the point, and 1/e is your x-coordinate of the point, so just substitute it into the original equation and you obtain -1/e, which is the y-coordinate of the minimum.

Reply to edit: Yes!!

 

[sasquatch]

That was obvious.. How stupid of me..