Question

Consider the function f(x) = 4x - x². Find the average rate of change over the given time intervals. 0.5 <= x <= 1, average rate of change =?

Answer 1

Answer:

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

Step-by-step 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.

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

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

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:

$\text{Average rate of change}=\frac{3-1.75}{1-0.5}$

$\text{Average rate of change}=\frac{1.25}{0.5}$

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

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

Answer 2

Answer:

your trash kid

Step-by-step explanation: