Question

What is the rate of change from x = π to x = 2π?

Answer 1

I suppose you mean average rate of change? Also, it's not clear what the function is, but I'd guess it's \(f(x)=-4\cos x\).

The average rate of change of a function \(f(x)\) over an interval \([a,b]\) is
\[\frac{f(b)-f(a)}{b-a}\]
In this case, \([a,b]=[\pi,2\pi]\), so the average rate of change is
\[\frac{-4\cos2\pi-(-4\cos\pi)}{2\pi-\pi}=\cdots\]