Q:

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?

Accepted Solution

A:
Answer:Hence, the rate of change between the interval of x = pi over 4 and x = pi over two is:[tex]\dfrac{-32}{\pi}[/tex]Step-by-step 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:[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]Here we have:[tex]a=\dfrac{\pi}{4}\ ,\ b=\dfrac{\pi}{2}\\\\and\\\\f(a)=1\ ,\ f(b)=-7[/tex]Hence, the rate of change from pi over 4 and pi over two is calculated as:[tex]=\dfrac{-7-1}{\dfrac{\pi}{2}-\dfrac{\pi}{4}}\\\\=\dfrac{-8}{\dfrac{\pi}{4}}\\\\\\=\dfrac{-32}{\pi}[/tex]