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

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