Question

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

Answer 1

The rate of change is m = -5.093

Explanation:

If we have a function f(x)

then the rate of change of this function in the interval [b, c] is:

`m = (f(c)-f(b))/(c-b)`

In this problem the function is:

`f(x) = -2cos(4x) - 3` y el intervalo es:

`x =(\pi)/(4)` to
`x =(\pi)/(2)`

First we must find
`f((\pi)/(4))` and
`f((\pi)/(2))`

`f((\pi)/(2)) = -2cos(4((\pi)/(2)))-3\\\\f((\pi)/(2)) = -2cos(2\pi)-3\\\\f((\pi)/(2)) = -5`

Now we find
`x =(\pi)/(4)`

`f((\pi)/(4)) = -2cos(4((\pi)/(4)))-3\\\\f((\pi)/(4)) = -2cos(\pi)-3\\\\f((\pi)/(4)) = -1`

Then:

`m = (f((\pi)/(2))-f((\pi)/(4)))/((\pi)/(2)-(\pi)/(4))\\\\m = (5-(-1))/((\pi)/(2)-(\pi)/(4))\\\\m = -5.093`