Continuity and DifferentiabilityHard

Question

If f(x) = (x - n)n(101-n) ; then =

Options

A.5050
B.
C.10010
D.

Solution

f(x) = (x - 1)100. (x - 2)2.99. (x - 3)3.98.....(x -100)100.1
Take log & than differentiate we get
Now
= 1 + 2 + 3 .... + 100 = 5050
∴ 

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