Let `f(x)=(x-1)^4(x-2)^n ,n in Ndot` Then `f(x)` has a maximum at `x=1` if `n` is odd a maximum at `x=1` if `n` is even a minimum at `x=1` if `n` is even 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)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value of n is________

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

Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1) . Then f(x) has local extremum at x = 1 , when n is (A) n = 2 (C) n = 4 (B) n = 3 (D) n = 5

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

The function f(x)=(x^2-4)^n(x^2-x+1),n in N , assumes a local minimum value at x=2. Then find the possible values of n

If f(x)=int_0^x(sint)/t dt ,x >0, then (a) f(x) has a local maxima at x=npi(n=2k ,k in I^+) (b) f(x) has a local minima at x=npi(n=2k ,k in I^+) (c) f(x) has neither maxima nor minima at x=npi(n in I^+) (d) (f)x has local maxima at x=npi(n=2k +1, k in I^+)

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

Show that f:Nto N, given by f (x) = x + 1 , if x is odd, f (x) = x -1, if x is even is both one-one and onto.

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to