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Answer 1 · 2017-06-09T19:36:31

#"SP": (1/3sqrt 2, 4/9sqrt2), (-1/3sqrt2, -4/9sqrt2)#

#f(x) = 2x-3x^3#

In order to find the stationary points if this function, we need to find #f'# and solve it for #x#.

#f'= 2-9x^2#

Let #f' = 0#

Then #2-9x^2 = 0#

#9x^2=2#

#x^2=2/9#

#x= +-sqrt2/3#

We have found the #x#-coordinates of the stationary points and we know need to find the #y#-coordinates.

#f(sqrt2/3) = 4/9sqrt2#

#f(-sqrt2/3) = -4/9sqrt2#

So the SP are #(1"/"3sqrt2, 4"/"9sqrt2) and (-1"/"sqrt2, -4"/"9sqrt2)#.