Consider the function `f(x)=xcosx-sinxdot` Then identify the statement which is correct. `f` is neither odd nor even. `f` is monotonic decreasing at `x=0` `f` has a maxima at `x=pi` `f` has a minima at `x=-pi`

Options

A. f is odd
B. f is monotonic decreasing at x=0
C. f has point of inflection at x=0
D. f has a maxima at x= `pi`

Answer

1,2,3

Explanation

`f(-x)=-xcos(-x)-sin(-x)=-xcosx+sinx=-f(x)`
`therefore` f(X) is odd function
`f(x) =-x sinx +cosx -coss x=-x sinx`
`f(x)=0 rarrx=npi,nimz`
`f(x) =-xcos x -sinx `
f(0)=0
`therefore x=0` is point of inflection
Thus at x=0 f(x) decreases
`f(pi)=pigt0`
`therefore x=pi` is point of minima