Question

Is `f(x)=cosx+cotx*sinx` increasing or decreasing at `x=pi/6`?

Answer 1

`f darr` at `x=pi/6`.

Explanation:

`f'(a)<0 rArr f darr` at `x=a`.

`f(x)=cosx+cotx*sinx=cosx+cosx=2cosx`

`rArr f'(x)=-2sinx rArr f'(pi/6)=-2*sin(pi/6)=-2*1/2=-1<0`.

Hence, `f darr` at `x=pi/6`.