Given mc008-1.jpg, what is the average rate of change in f(x) over the interval [1, 5]?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 345 People

Answered by maham237 @ 25/12/2020

we know that

The average rate of change of the function f(x) over the interval [a,b] is equal to

$\frac{(f(b)-f(a))}{(b-a)}$

in this problem

$f(x)=17 -x^{2}$

interval [a,b]----------> $[1,5]$

for $x=1$

$f(1)=17 -1^{2} =16$

for $x=5$

$f(5)=17 -5^{2} =-8$

substitute the values

$\frac{(f(b)-f(a))}{(b-a)}$

$\frac{(-8-16)}{(5-1)}$

$=-6$

therefore

the answer is

The average rate of change is equal to $-6$

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