An extremum of the function `f(x)=(2-x)/picospi(x+3)+1/(pi^2)sinpi(x+3)` where x `in (0,4)` occurs at (a) `x=1` (b) `x=2` (c) `x=3` (d) `x=pi`

Options

A. x=1
B. x=2
C. x=3
D. x=`pi`

Answer

1,3

Explanation

`f(x)=(2-x)/(pi)cospi(x+3)+(1)/(pi^(2))sinpi(x+3)`
`f(X)=-(1)/(pi)cos pi(x+3)-(2-x)sinpi(x+3)`
`=(x-2)sinpi(x+3)=0(let)`
`therefore x=2,1,3`
`f(x)=sinpi(x+3)+pi(x-2)cospi(x+3)`
`f(X)=-pilt0f(2)=0f(3)=pigt0`
Therefore x=1 is a maximum and x =3 is a minimum hence x=2 is the point of infleciton