stationary points??

[scatteam_2]

Find the coordinates of the stationary point on the curve with equation y = x^2loge(1/x) and determine the
nature of the stationary point

the derivative is -2xlogex - x

THIS IS A NON CALCULATOR QUESTION

i found x = e^-1/2

but how do u do the gradient test
ur meant to pick one value above and below e^-1/2
but this value seems very hard to work with

[brightsky]

Derivative is . Stationary points given by:





or

Solution:

To test, substitute x = 1/2, dy/dx = -1 ln(1/2) - 1/2 > 0 . Substitute x = 1, dy/dx = -1 [/tex]

So it's a maximum.

EDIT: Sorry, silly mistake. xD