The demand, D, for a new rollerball pen is given by D= 0.007p3 - 0.8p? + 170p, where p is the price in dollars. a) Find the rate of change of quantity with respect to price, dD/dp. b)How many units will consumers want to buy when the price is $25 per unit? c) Find the rate of change at p= 25, and interpret this result. djwould you expect dD/dp to be positive or negative? dD dp
The demand, D, for a new rollerball pen is given by D= 0.007p3 - 0.8p? + 170p, where p is the price in dollars. a) Find the rate of change of quantity with respect to price, dD/dp. b)How many units will consumers want to buy when the price is $25 per unit? c) Find the rate of change at p= 25, and interpret this result. djwould you expect dD/dp to be positive or negative? dD dp
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Transcription for Educational Website
#### Demand Function Analysis for Rollerball Pen
The demand, \( D \), for a new rollerball pen is described by the equation:
\[ D = 0.007p^3 - 0.8p^2 + 170p \]
where \( p \) is the price in dollars.
**Questions:**
a) **Find the rate of change of quantity with respect to price, \( \frac{dD}{dp} \).**
b) **How many units will consumers want to buy when the price is $25 per unit?**
c) **Find the rate of change at \( p = 25 \), and interpret this result.**
d) **Would you expect \( \frac{dD}{dp} \) to be positive or negative?**
**Solution Steps:**
- **a) Calculate \( \frac{dD}{dp} \):**
- Differentiate the function \( D \) with respect to \( p \).
There are no graphs or diagrams accompanying this text.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F697964e5-5ccc-4085-bdf2-5f02d7884956%2Fa99bca69-7bbd-4136-a10f-c1c0ddce8715%2F0odqw8o_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Website
#### Demand Function Analysis for Rollerball Pen
The demand, \( D \), for a new rollerball pen is described by the equation:
\[ D = 0.007p^3 - 0.8p^2 + 170p \]
where \( p \) is the price in dollars.
**Questions:**
a) **Find the rate of change of quantity with respect to price, \( \frac{dD}{dp} \).**
b) **How many units will consumers want to buy when the price is $25 per unit?**
c) **Find the rate of change at \( p = 25 \), and interpret this result.**
d) **Would you expect \( \frac{dD}{dp} \) to be positive or negative?**
**Solution Steps:**
- **a) Calculate \( \frac{dD}{dp} \):**
- Differentiate the function \( D \) with respect to \( p \).
There are no graphs or diagrams accompanying this text.
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