Question

Suppose the function f is defined by

f(x) = – 1* x^2 – 4* x + 2.
In the text box below, enter the Average Rate of Change of f as x goes from 1 to 3. Your answer should be a number; do not enter letters or other symbols in the text box. Your answer must be exact, please do not round off your answer. For example, do not round off 1/3 to be .33. After entering your answer, click the Save Answer button.

Answer 1

-8

Explanation:

GIven a function
`f(x)`, the rate of change of the function over an interval
`x_1,x_2` is given by

`r=(f(x_2)-f(x_1))/(x_2-x_1)`

where

`f(x_2)` is the value of the function calculated in
`x_2`

`f(x_1)` is the value of the function calculated in
`x_1`

In this problem, the function is

`f(x)=-x^2-4x+2`

The interval is

`x_1=1\\x_2=3`

So we have:

`f(x_1)=f(1)=-(1)^2-4(1)+2=-3`

`f(x_2)=f(3)=-(3)^2-4(3)+2=-19`

Therefore, the rate of change of the function is

`r=(-19-(-3))/(3-1)=(-16)/(2)=-8`