suppose that the total profit in hundreds of dollars from selling x items is given by p(x)=4x² - 7x + 9…

suppose that the total profit in hundreds of dollars from selling x items is given by p(x)=4x² - 7x + 9. complete parts a through d below.\na. find the average rate of change of profit as x changes from 3 to 5.\n$ per item

suppose that the total profit in hundreds of dollars from selling x items is given by p(x)=4x² - 7x + 9. complete parts a through d below.\na. find the average rate of change of profit as x changes from 3 to 5.\n$ per item

Answer

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $P(x)=4x^{2}-7x + 9$, $a = 3$, and $b = 5$.

Step2: Calculate $P(3)$

Substitute $x = 3$ into $P(x)$: $P(3)=4\times3^{2}-7\times3 + 9=4\times9-21 + 9=36-21 + 9=24$.

Step3: Calculate $P(5)$

Substitute $x = 5$ into $P(x)$: $P(5)=4\times5^{2}-7\times5 + 9=4\times25-35 + 9=100-35 + 9=74$.

Step4: Calculate the average rate of change

$\frac{P(5)-P(3)}{5 - 3}=\frac{74 - 24}{2}=\frac{50}{2}=25$. Since $P(x)$ is in hundreds of dollars, the average rate of change is $25\times100=$2500$ per item.

Answer:

$2500$