For the function 
.Prove that f’ (1) =100 f’ (0).
Given function is
Since, 
At x = 0
f’(0) = 0 + 0 + … + 0 + 1
f’(0) = 1
At x = 1
f’(1) = 199 + 198 + … + 1 + 1 = [1 + 1 ….+ 1] 100 times = 1 × 100 = 100
Thus f’(1) = 100 f’(0)
5
For the function .Prove that f’ (1) =100 f’ (0).
Given function is
Since,
At x = 0
f’(0) = 0 + 0 + … + 0 + 1
f’(0) = 1
At x = 1
f’(1) = 199 + 198 + … + 1 + 1 = [1 + 1 ….+ 1] 100 times = 1 × 100 = 100
Thus f’(1) = 100 f’(0)