Is there any direct way of proving that a function is increasing within a given interval?

Say the function f(x)=cos(2x+ π/4) and i have to prove its an increasing function within (3π/8,7π/8). The books do it as finding f'(x) and putting it greater than 0 to find the total interval within which the function is increasing and finding that the given interval is a sub interval of the big interval. Is there a more direct way of doing this where you do something with the given interval itself? Often times such questions give me a bit of trouble. Any advice would be appreciated 🙏