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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.

Respuesta :

skyluke89

Answer:

-8

Step-by-step explanation:

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

[tex]r=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

where

[tex]f(x_2)[/tex] is the value of the function calculated in [tex]x_2[/tex]

[tex]f(x_1)[/tex] is the value of the function calculated in [tex]x_1[/tex]

In this problem, the function is

[tex]f(x)=-x^2-4x+2[/tex]

The interval is

[tex]x_1=1\\x_2=3[/tex]

So we have:

[tex]f(x_1)=f(1)=-(1)^2-4(1)+2=-3[/tex]

[tex]f(x_2)=f(3)=-(3)^2-4(3)+2=-19[/tex]

Therefore, the rate of change of the function is

[tex]r=\frac{-19-(-3)}{3-1}=\frac{-16}{2}=-8[/tex]

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