Suppose a product's revenue function is given by R(q)=-2q^2+800_q 
.

Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.)

 MR(q)=  

To find the marginal revenue function, \( MR(q) \), we need to differentiate the revenue function \( R(q) \) with respect to \( q \).

The revenue function is:
\[
R(q) = -2q^2 + 800q
\]

Now, take the derivative of \( R(q) \) with respect to \( q \):
\[
MR(q) = \frac{d}{dq} \left( -2q^2 + 800q \right)
\]

Step-by-step:
- The derivative of \( -2q^2 \) is \( -4q \) (using the power rule: \( \frac{d}{dq} (q^n) = nq^{n-1} \)).
- The derivative of \( 800q \) is \( 800 \) (since the derivative of a linear term \( kq \) is just \( k \)).

So, the marginal revenue function is:
\[
MR(q) = -4q + 800
\]

This is the simplified expression for the marginal revenue function.

Let me know if you'd like further details or have any questions!

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Here are 5 questions to expand on this topic:
1. What is the significance of the marginal revenue function?
2. How does marginal revenue relate to the demand function?
3. At what quantity \( q \) is the marginal revenue equal to zero?
4. How would you find the maximum revenue from this function?
5. Can marginal revenue be negative? What does it mean in this case?

**Tip:** Marginal revenue helps you determine how much revenue changes with each additional unit produced or sold.

Suppose a product's revenue function is given by R(q) = -2q^2 + 800q. Find an expression for the marginal revenue function, simplify it, and record your result in the box below.

Learn how to find the marginal revenue function from a quadratic revenue function R(q) = -2q^2 + 800q. This problem covers differentiation concepts, including the power rule and interpreting marginal revenue. Suitable for students in Grades 11-12 or early college.

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