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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.

1 Answer

6 votes

Answer:

-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

User Lmno
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