Consider the function $y=-x^2+4$ . What is the average rate of change from $[1, 5]$ ?

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Answer 1 · 2017-03-03T11:14:14

$-6$

The average rate of change of a continuous function,
$f(x)$ , on a closed interval $[a,b]$ is given by

$bar f(x) =(f(b)-f(a))/(b-a)$

So the average rate of change of the function $f(x)=-x^2+4$ on $[1,5]$ is:

$Aroc = ( f(5)-f(1) ) / ( 5-1 )$
$" " = ( ( -25+4) - (-1+4) ) / 4$
$" " = ( ( -21) - (3) ) / 4$
$" " = -24/4$
$" " = -6$

Consider the function y=-x^2+4y=-x^2+4. What is the average rate of change from [1, 5][1, 5]?