Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

The graph below shows a company’s profit f(x) in dollars, depending on the price of goods x, in dollar’s, being sold by the company: Part A: What do the x-intercepts and maximum value of the graph represent in context of the disrobed situation?Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit for the company in the situation described?Part C: What is an approximate average rate of change of the graph from x=1 to x=3, and what does this rate represent in context of the described situation?

The Graph Below Shows A Companys Profit Fx In Dollars Depending On The Price Of Goods X In Dollars Being Sold By The Company Part A What Do The Xintercepts And class=

Sagot :

We will have the following:

Part A:

The x-intercepts represent the prices of the goods than wen sold represent no net gain or loss.

The maximum value represents the price at which there will be a maximum profit.

Part B:

We will have that the increasing and decreasing intervals are respectively:

[tex]I_{\text{increaing}}=(-\, \infty,3)[/tex][tex]I_{\text{decreasing}}=(3,\infty)[/tex]

They tells us respectively that:

Increasing: The greater the price the greater the profit.

Decreasing: The greater the price the smaller the profit.

Part C:

We determine the equation of the parabola. We can see that it's vertex is located at (3, 120), we can also see that the parabola passes by the origin (0, 0); so:

[tex]f(x)=a(x-3)^2+120\Rightarrow0=a(0-3)^2+120[/tex][tex]\Rightarrow0=9a+120\Rightarrow9a=-120\Rightarrow a=-\frac{40}{3}[/tex]

So, the equation that represents the parabola is:

[tex]f(x)=-\frac{40}{3}(x-3)^2+120[/tex]

Then, we will determine the average rate of change as follows:

[tex]\text{average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]

So:

[tex]\text{average rate of change}=\frac{(-40/3((3)-3)^2+120)-(-40/3((1)-3)^2+120)}{3-1}[/tex][tex]\text{average rate of change}=\frac{80}{3}\Rightarrow average\text{ rate of change}\approx26.67[/tex]

So, the avereage rate of change for the graph from x = 1 to x = 3 is exactly 80/3, that is approximately 26.67.

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.