Question

Find the average rate if change in the function f(x) = x^2 +2 over the interval x= -5 to x= -2

Answer 1

Average rate of change of function f(x) = x^2 +2 over the interval x= -5 to x= -2 is -7

Step-by-step explanation:

We need to find the average rate if change in the function f(x) = x^2 +2 over the interval x= -5 to x= -2

The formula used to find the change of average rate is:

$Rate\,\,of\,\,change=\frac{f(b)-f(a)}{b-a}$

Where b= -2 and a= -5

Finding f(b) and f(a)

f(b)=f(-2)=(-2)^2+2=4+2=6

f(a)=f(-5)=(-5)^2+2=25+2=27

Putting values in the formula:

$Rate\,\,of\,\,change=\frac{f(b)-f(a)}{b-a}\\Rate\,\,of\,\,change=\frac{6-27}{(-2)-(-5)}\\Rate\,\,of\,\,change=\frac{-21}{-2+5}\\Rate\,\,of\,\,change=\frac{-21}{3}\\Rate\,\,of\,\,change=-7$

Average rate of change of function f(x) = x^2 +2 over the interval x= -5 to x= -2 is -7

Keywords: Average Rate of change

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