Question

What is the rate of change for f(x) = −2 cos 4x − 3 on the interval from x = 0 to x = pi over 4?

Answer 1

You probably mean *average* rate of change. In that case, you have
\[\text{average rate of change}=\frac{f(b)-f(a)}{b-a}\]
where \([a,b]=\left[0,\dfrac{\pi}{4}\right]\) is the given interval.