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You have a job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p · f(p), depending on the price. Match the mathematical expression below with the best interpretation. I. f'(15)= 3 1. If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. If the price increases from $15 to $20 then the company expects to sell 3 hundred more gadgets. 4. When the company sells 3 hundred gadgets, the price is $60 each. 5. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets. Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a sentence or two, briefly explain if this statement is necessarily true or not.

You have a job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p · f(p), depending on the price. Match the mathematical expression below with the best interpretation. I. f'(15)= 3 1. If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. If the price increases from $15 to $20 then the company expects to sell 3 hundred more gadgets. 4. When the company sells 3 hundred gadgets, the price is $60 each. 5. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets. Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a sentence or two, briefly explain if this statement is necessarily true or not.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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You have a job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p · f(p), depending on the price. Match the mathematical expression below with the best interpretation. I. f' (15) = 3 1. If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. If the price increases from $15 to $20 then the company expects to sell 3 hundred more gadgets. When the company sells 3 hundred gadgets, the price is $60 each. 5. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets. Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a sentence or two, briefly explain if this statement is necessarily true or not. 4.
Transcribed Image Text:You have a job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p · f(p), depending on the price. Match the mathematical expression below with the best interpretation. I. f' (15) = 3 1. If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. If the price increases from $15 to $20 then the company expects to sell 3 hundred more gadgets. When the company sells 3 hundred gadgets, the price is $60 each. 5. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets. Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a sentence or two, briefly explain if this statement is necessarily true or not. 4.
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