i have a function

f(x)= 1 for x=1/n

f(x)=0 for otherwise

n is a natural number

prove that f(x) is defferentiable [0,1]

?

first i tried to prove that there are finite number of discontenuety points

n>1/a so 0<1/n<a

then the book says that there at most n-1 discontinuty ponts

dont know how they got it from the last innequality

?