Question

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

Answer 1

Increasing

Explanation:

To find if a function `f(x)` is increasing or deceasing at a point `f(a)`, we take the derivative `f'(x)` and find `f'(a)`/

If `f'(a)>0` it is increasing
If `f'(a)=0` it is an inflection
If `f'(a)<0` it is decreasing

`f(x)=cosx+sinx`

`f'(x)=-sinx+cosx`

`f'(pi/6)=cos(pi/6)-sin(pi/6)=(-1+sqrt(3))/2`

`f'(pi/6)>0`, so it is increasing at `f(pi/6)`