Explaining the meaning of a derivative

  • Thread starter Thread starter Dramacon
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary
SUMMARY

The discussion centers on calculating the derivative of revenue with respect to price, specifically using the formula R=30P-2P^2. The derivative, dR/dP, is determined to be 30-4P. This derivative represents the rate of change of revenue as the price per item changes, which is a fundamental concept in understanding marginal revenue in economics.

PREREQUISITES
  • Understanding of basic calculus, specifically differentiation.
  • Familiarity with revenue functions in economics.
  • Knowledge of the concept of marginal revenue.
  • Ability to interpret mathematical derivatives in a business context.
NEXT STEPS
  • Study the concept of marginal revenue in detail.
  • Learn how to apply derivatives in economic models.
  • Explore the implications of price elasticity on revenue.
  • Investigate the relationship between cost functions and revenue maximization.
USEFUL FOR

Students in economics, business analysts, and anyone interested in applying calculus to real-world revenue scenarios will benefit from this discussion.

Dramacon
Messages
14
Reaction score
0

Homework Statement


As the result of a survey, the marketing director of a company found that the revenue, $R, from selling n produced items at $P is given by the rule R=30P-2P^2

Find dR/dP and explain what it means

Homework Equations


I've found the dR/dP, however, I'm unsure of what this means in terms of the criteria in the question


The Attempt at a Solution



dR/dP= 30-4P

Edit:
Don't worry! Just solved it, it's rate of change of revenue with respect to price. I'm so silly
 
Last edited:
Physics news on Phys.org
Have you studied the concept of marginal revenue?
 

Similar threads

Finding the derivative of a revenue function
  • · Replies 7 ·
Replies
7
Views
3K
Calculating Marginal Revenue: Qx-y Formula
  • · Replies 4 ·
Replies
4
Views
2K
What is the optimal number of items to produce for maximum profit in business?
  • · Replies 2 ·
Replies
2
Views
1K
Derivation of the momentum-to-the-power-of-n operator
  • · Replies 3 ·
Replies
3
Views
2K
Calc student stuck on business application: revenue for 1 additional item
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Atmospheric Density vs Altitude in an O'Neil Cylinder
  • · Replies 1 ·
Replies
1
Views
3K
Derive an expression for the price of a pen in terms of p
  • · Replies 6 ·
Replies
6
Views
2K
Optimization: Maximizing Profit
  • · Replies 5 ·
Replies
5
Views
8K
Demand and revenue question: help?
  • · Replies 2 ·
Replies
2
Views
2K
Linear approximation of bus revenue
  • · Replies 4 ·
Replies
4
Views
3K