Question

Use the graph below to answer the question that follows: graph of the curve that passes through the following points 0, negative 3 and pi over 4, 1 and pi over 2, negative 7 and 3 pi over 4, 1 and pi, negative 3 What is the rate of change between the interval of x = pi over 4 and x = pi over two?

Answer 1

Hence, the rate of change between the interval of x = pi over 4 and x = pi over two is:

`(-32)/(\pi)`

Explanation:

We are given the data about the graph as:

graph of the curve that passes through the following points 0, negative 3 and pi over 4, 1 and pi over 2, negative 7 and 3 pi over 4, 1 and pi, negative 3 .

We know that the rate of change of a graph or a function f(x) in the interval a to b is given by:

`(f(b)-f(a))/(b-a)`

Here we have:

`a=(\pi)/(4)\ ,\ b=(\pi)/(2)\\\\and\\\\f(a)=1\ ,\ f(b)=-7`

Hence, the rate of change from pi over 4 and pi over two is calculated as:

`=(-7-1)/((\pi)/(2)-(\pi)/(4))\\\\=(-8)/((\pi)/(4))\\\\\\=(-32)/(\pi)`