Let `f(x)=(x-1)^4(x-2)^n ,n in Ndot` Then `f(x)` has (a) a maximum at `x=1` if `n` is odd (b) a maximum at `x=1` if `n` is even (c) a minimum at `x=1` if `n` is even (d) a minima at `x=2` if `n` is even

If f(x)=(sin^2x-1)^("n"),"" then x=pi/2 is a point of local maximum, if n is odd local minimum, if n is odd local maximum, if n is even local minimum, if n is even

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then f has

Let f(x)=(x-1)(x-2)(x-3)...(x-n),n in N ,a n d f'(n)=5040. Then the value of n is________

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N , has a local minimum at x=pi/6 . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number

f(x) is cubic polynomial with f(x)=18 and f(1)=-1 . Also f(x) has local maxima at x=-1 and f^(prime)(x) has local minima at x=0 , then (A) the distance between (-1,2)a n d(af(a)), where x=a is the point of local minima is 2sqrt(5) (B) f(x) is increasing for x in [1,2sqrt(5]) (C) f(x) has local minima at x=1 (D)the value of f(0)=15

Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f decreases on [1,oo] (c) f has a minimum at x=1 (d) f has neither maximum nor minimum

If f(x+1)+f(x-1)=2f(x) and f(0)=0, then find f(n),n in N , is

If f(x)=prod_(n=1)^(100)(x-n)^(n(101-n)) ; then (f(101))/(f'(101))=

Let f(x)=lim_(nto oo) 1/n((x+1/n)^(2)+(x+2/n)^(2)+……….+(x+(n-1)/n)^(2)) Then the minimum value of f(x) is