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
∴

Create a free account to view solution

View Solution Free

Topic: Continuity and Differentiability·Practice all Continuity and Differentiability questions

More Continuity and Differentiability Questions

If f(4) = g(4) = 2 ; f′(4) = 9 ; g′(4) = 6 then is equal to -...Let $f: \mathbb{R} \rightarrow (0,\infty)$ be a twice differentiable function such that $f(3) = 18$, $f'(3) = 0$, and $f...There exists a function f(x) satisfying f(0) = 1, f′(0) = - 1 f(x) > 0 for all x and...If y2 = p(x) is a polynomial of degree 3, then equals...Which of the following could be the sketch graph of y = (x lnx) ?...