The function is: $f(x)= \sin(x)-\cos(x)$ over the interval $[-\pi, \pi]$.
To evaluate the increasing / decreasing portion of the function I look at where the first derivative is $>0$. $f'(x)=\cos(x) + \sin(x)$. I want to know where this is $>0$ without a graphing calculator.
I'm stuck here. I know that the derivative would be greater than zero in Quadrant 1. I know that the derivative would be $<0$ in Q3. I can intuitively think of where in Q2 and Q3 that the derivative would be $>0$, but I don't know how to show this mathematically. I also don't think I totally understand the significance of the interval, since the interval is essentially over the entire $0-2\pi$ range but stated in this unusual manner.