Question

Is `f(x)=sinx-cosx` increasing or decreasing at `x=0`?

Answer 1

`f(x)=sinx-cosx` is increasing at `x=0`

Explanation:

Whether a function `f(x)` is increasing or decreasing at `x=0`, is determined by the value of its derivative at `x=0`.

As `f(x)=sinx-cosx`

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

and at `x=0`, `f'(0)=cos0+sin0=1+0=1`

As `f'(0)>0`, `f(x)` is increasing at `x=0`
graph{sinx-cosx [-5, 5, -2.5, 2.5]}