Consider the function f(x) = 4x - xÂ². Find the average rate of change over the given time intervals. 0.5 <= x <= 1, average rate of change =?

Question

asked Oct 19, 2021 20.1k views

2 Answers

Derek Chiang · Answer 1 · 2021-10-25T12:32:33+0000

Answer:

$\text{Average rate of change}=2.50$

Explanation:

We have been given a function
f(x)=4x-x^2 . We are asked to find average rate of change over the given time intervals of
$0.5\leq x\leq 1$ .

We will average rate change formula to solve our given problem.

$\text{Average rate of change}=(f(b)-f(a))/(b-a)$

$\text{Average rate of change}=(f(1)-f(0.5))/(1-0.5)$

Let us find f(1) and f(0.5) using our given function.

f(1)=4(1)-(1)^2

f(1)=4-1

f(1)=3

f(0.5)=4(0.5)-(0.5)^2

f(0.5)=2-0.25

f(0.5)=1.75

Upon substituting these values in average rate of change formula, we will get:

$\text{Average rate of change}=(3-1.75)/(1-0.5)$

$\text{Average rate of change}=(1.25)/(0.5)$

$\text{Average rate of change}=2.50$

Therefore, the average rate of change over the interval
$0.5\leq x\leq 1$ would be 2.50.