Answer:
The rate of change is m = -5.093
Step-by-step explanation:
If we have a function f(x)
then the rate of change of this function in the interval [b, c] is:
[tex]m = \frac{f(c)-f(b)}{c-b}[/tex]
In this problem the function is:
[tex]f(x) = -2cos(4x) - 3[/tex] y el intervalo es:
[tex]x =\frac{\pi}{4}[/tex] to [tex]x =\frac{\pi}{2}[/tex]
First we must find [tex]f(\frac{\pi}{4})[/tex] and [tex]f(\frac{\pi}{2})[/tex]
[tex]f(\frac{\pi}{2}) = -2cos(4(\frac{\pi}{2}))-3\\\\f(\frac{\pi}{2}) = -2cos(2\pi)-3\\\\f(\frac{\pi}{2}) = -5[/tex]
Now we find [tex]x =\frac{\pi}{4}[/tex]
[tex]f(\frac{\pi}{4}) = -2cos(4(\frac{\pi}{4}))-3\\\\f(\frac{\pi}{4}) = -2cos(\pi)-3\\\\f(\frac{\pi}{4}) = -1[/tex]
Then:
[tex]m = \frac{f(\frac{\pi}{2})-f(\frac{\pi}{4})}{\frac{\pi}{2}-\frac{\pi}{4}}\\\\m = \frac{5-(-1)}{\frac{\pi}{2}-\frac{\pi}{4}}\\\\m = -5.093[/tex]
