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given f(x) = x/3 - x

for maxima and minima

f '(x) = 0

so f '(x) = x- 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

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