Find all relative extrema of the function If an answer does

Find all relative extrema of the function. (If an answer does not exist, enter DNE.)

g(x) =g(x) =

(1/3)x³ x

relative maximum	(x, y)	=
relative minimum	(x, y)	=

Solution

g(x) = x^3/3 -x

find derivative of g(x) :

g\'(x) = x^2 -1 ; g\'(x) =0

So, x^2 -1 =0

x = +1 , -1

g\"(x) = 2x

Now

So, Relative maximum : at x= -1; f(-1) = -1/3 +1 = 2/3

So, Relative maximum : at x= 1; f(1) = 1/3 -1 = -2/3

So, real. maximum -----( -1, 2/3)

real. minimum -------( 1 , -2/3)