suppose that the total profit in hundreds of dollars from selling x items is given by p(x)=4x^{2}-7x + 9…

suppose that the total profit in hundreds of dollars from selling x items is given by p(x)=4x^{2}-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$2500 per item\nb. find the average rate of change of profit as x changes from 3 to 4.\n$ per item

suppose that the total profit in hundreds of dollars from selling x items is given by p(x)=4x^{2}-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$2500 per item\nb. find the average rate of change of profit as x changes from 3 to 4.\n$ 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 $\frac{f(b)-f(a)}{b - a}$.

Step2: Calculate $P(4)$ and $P(3)$

First, find $P(x)=4x^{2}-7x + 9$. For $x = 3$, $P(3)=4\times3^{2}-7\times3 + 9=4\times9-21 + 9=36-21 + 9=24$. For $x = 4$, $P(4)=4\times4^{2}-7\times4 + 9=4\times16-28 + 9=64-28 + 9=45$.

Step3: Calculate the average rate of change

The average rate of change from $x = 3$ to $x = 4$ is $\frac{P(4)-P(3)}{4 - 3}=\frac{45-24}{1}=21$. Since the profit is in hundreds of dollars, the average rate of change is $$2100$ per item.

Answer:

$2100$