Question

A paint manufacturing company estimates that it can sell $g=f(p)$ gallons of paint at a price of $p$ dollars. (a) What are the units of $d g / d p ?$ (b) In practical terms, what does de/dp mean in this case? (c) What can you say about the sign of $d g / d p ?$ (d) Given that $d g /\left.d p\right|_{p=10}=-100 .$ what can you say about the effect of increasing the price from $\$ 10$ per eallon to $\$ 11$ per pallon?

          A paint manufacturing company estimates that it can sell $g=f(p)$ gallons of paint at a price of $p$ dollars.
(a) What are the units of $d g / d p ?$
(b) In practical terms, what does de/dp mean in this case?
(c) What can you say about the sign of $d g / d p ?$
(d) Given that $d g /\left.d p\right|_{p=10}=-100 .$ what can you say about the effect of increasing the price from $\$ 10$ per eallon to $\$ 11$ per pallon?
        
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Added by Ruben F.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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A paint manufacturing company estimates that it can sell $g=f(p)$ gallons of paint at a price of $p$ dollars. (a) What are the units of $d g / d p ?$ (b) In practical terms, what does dg/dp mean in this case? (c) What can you say about the sign of $d g / d p ?$ (d) Given that $d g /left.d p ight|_{p=10}=-100 .$ what can you say about the effect of increasing the price from $$ 10$ per gallon to $$ 11$ per gallon?
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Transcript

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00:01 So a pay manufacturer estimates it can sell g equals f of p gallon of paint at the price of p dollars.
00:06 So what are the units of dg and ddp? so the units are going to be gallons of paint that have been sold.
00:15 And the pdp is the units is going to be the price in dollars.
00:22 So the units are going to be dollars and gallons...
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