given f(x) = x3 /3 - x
for maxima and minima
f '(x) = 0
so f '(x) = x2 - 1 = 0
ie x = 1,-1
f ''(x) = 2x
here
f ''(1) = 2 >0 (positive)
f ''(-1) = -2 <0 (negative)
we know if f ''(a) >0 then will be minima at x=a
and if f ''(a) <0 then will be maxima at x=a
so here at x=1 f(x) has minimum value