Explaining the meaning of a derivative

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In summary, a derivative is a mathematical concept that measures the instantaneous rate of change of one variable with respect to another. It is important because it allows for the analysis of functions and has practical applications in fields such as physics, economics, and engineering. The derivative can be calculated using the limit definition or derivative rules and formulas, and its geometric interpretation is the slope of the tangent line to a curve. A real-life application of derivatives includes calculating velocity and acceleration in physics, analyzing supply and demand curves in economics, and optimizing designs in engineering."
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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:
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Have you studied the concept of marginal revenue?
 

1. What is a derivative?

A derivative is a mathematical concept that represents the instantaneous rate of change of one variable with respect to another. In simpler terms, it measures how much a function is changing at a specific point.

2. Why is the derivative important?

The derivative is important because it allows us to analyze the behavior of functions and make predictions about their future values. It has many practical applications in fields such as physics, economics, and engineering.

3. How is the derivative calculated?

The derivative is calculated using the limit definition, which involves taking the slope of a tangent line at a specific point on a curve. It can also be calculated using derivative rules and formulas for different types of functions.

4. What is the geometric interpretation of a derivative?

The geometric interpretation of a derivative is the slope of the tangent line to a curve at a specific point. This slope represents the rate of change of the function at that point.

5. Can you give an example of a real-life application of derivatives?

One example of a real-life application of derivatives is in physics, where it is used to calculate the velocity and acceleration of an object. It is also used in economics to analyze supply and demand curves and in engineering to optimize designs and improve efficiency.

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