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

Options

A. local maximum , if n is odd
B. local minimum, if n is odd
C. local maximum if n is even
D. local minimum if n is even

Answer

1,4

Explanation

`f(x)=(sin^(2)x-1)^(n)`
`f((pi)/(2))=0`
`f(pi)/(2)=rarr0^(-)(n) and f((pi)/(2))=rarr0^(-)(n)`
if n is even `f(pi^(+))/(2)and f(pi^(+))/(2)gt0` Then `x=(pi)/(2)` is the point of minima
If n is odd `f(pi)/(2)`and `f(pi)/(2)lt0` .Then `x =(pi)/(2)` is the point of maxima