[prism941]

what formula would I use for R(x)=400+x^2? Size increases from 20 to 30.

[Unknown008]

I'm sorry, I don't understand your question.

What increases from 20 to 30?
What is r(x) = 400 + x^2?
What are you looking for?

Is r(x) an area, with its function being 400+x^2, and that area increases from 20 to 30?

It would be best for you to post the whole question, and say what you did already, and what you don't understand.

[prism941]

the revenue function for the annual super bowl party is defined as follows: R(x)=400+x^2; where x is the increase in group size beyond 10 people. What is the average rate of change of revenue if the group size increases from 20 to 30.

[Unknown008]

Ok, so 'x' is increasing.

Change in 'x' is 10 (from 30 to 20). This is denoted by

Now, you have R(x) = 400 + x^2.

Using Chain rule, you can find the rate of change of revenue, which is denoted by



So, find dR/dx. You have the value of x, which is 20 (you take the initial value of x) You can find the value of dR/dx.

Then, you have the value of dx/dt.

Multiply both values together to get the rate of change of your revenue!

i hope this helped! :)

[Unknown008]

Please, do not start another thread to ask how to differentiate. You could have asked that here, or on the threads that you already posted before. I assumed that you knew how to differentiate, but you should have said that you have difficulty in finding the derivative of a function!



Ok, differentiating y, we get:



When you differentiate, the derivative of is :

So, x^2 becomes 2x.

Multiply the coefficient by the power, then decrease the power by one.

x^3 becomes 3x^2
x^4 becomes 4x^3

Now, with a coefficient:

2x^2 becomes (2)(2)x = 4x
2x^3 becomes (2)(3)x^2 = 6x^2
3x^4 becomes (3)(4)x^3 = 12x^3

Is it OK? :)