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 the function f(x)=(4sin ^2 x-1)^n(x^2-x+1)n in N has a local maximum at x= pi //6 then n

The function f(x)=(4sin^(2)x-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 ( ) n is odd prime number (d) n is any natural number

let f(x)=(x^(2)-1)^(n)(x^(2)+x-1) then f(x) has local minimum at x=1 when

If p(x)=(1+x^(2)+x^(4)+...+x^(2n-2))/(1+x+x^(2)+...+x^(n-1)) is a polomial in x, then find possible value of n.

Let f(x)=(x-2)^2x^n, n in N Then f(x) has a minimum at

If f(x)=x^(n)&f'(1)=10, find the value of n.

Let f(x)=x^(3)-12x be function such that the equation |f(|x|)|=n(n in N) has exactly 6 distinct real roots then number of possible values of n are

If the function f(x)={A x-B ,xlt=1 3x ,1