Test f(x)={x} for the existence of alocal maximum and minimum at x=1, where{.} represents the fractional part function.

Explanation

We know that f(x)={x} is discontinous at integral values of x and hence at x=1
Now f(1)=0 and `f(1^(+)) =0^(+)` and `C=1^(-)`
Thus `f(1)ltf(1^(+))` and `F(1)ltf(1^(-))`
so x=1 is point of minima.